Can anyone help with these precalculus questions? [on hold]

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I'm having trouble with 4-6. The answers are on the next page of the PDF. I need to understand how they arrived at those answers.



Problems




trigonometry logarithms inverse-function




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put on hold as off-topic by Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 3




    It's better to post one question at a time, write the problem out in the body of your question, and explain what you have tried, what you're stuck on, and what your thoughts are about it.
    – littleO
    yesterday






  • 1




    Welcome to Stackexchange. See here and here for more information on how to improve your post, as well as here and here for information on how to write math on this site.
    – Simply Beautiful Art
    yesterday










  • For (4) replace $x$ by $f^-1(x)$. You get $x=f(f^-1(x))=frace^f^-1(x)+1e^f^-1(x)-1$. Now solve for $e^f^-1(x)$ first. To do this, multiply by the denominator. You get $x(e^f^-1(x)-1)=e^f^-1(x)+1$. Group the $e^f^-1(x)$ to get $(x-1)e^f^-1(x)=1+x$. Therefore $e^f^-1(x)=fracx+1x-1$. Finally, take natural logarithms on both sides: $f^-1(x)=lnleft(fracx+1x-1right)$.
    – spiralstotheleft
    yesterday










  • For (6.a) multiply and divide by $sqrtx+1-sqrtx$. For (6.b) use that $sin(2x)=2sin(x)cos(x)$, that $1-cos^2(x)=sin^2(x)$, and that $cot(x)=fraccos(x)sin(x)$. Everything simplifies.
    – spiralstotheleft
    yesterday














up vote
-4
down vote

favorite












I'm having trouble with 4-6. The answers are on the next page of the PDF. I need to understand how they arrived at those answers.



Problems




trigonometry logarithms inverse-function




share|cite|improve this question











put on hold as off-topic by Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 3




    It's better to post one question at a time, write the problem out in the body of your question, and explain what you have tried, what you're stuck on, and what your thoughts are about it.
    – littleO
    yesterday






  • 1




    Welcome to Stackexchange. See here and here for more information on how to improve your post, as well as here and here for information on how to write math on this site.
    – Simply Beautiful Art
    yesterday










  • For (4) replace $x$ by $f^-1(x)$. You get $x=f(f^-1(x))=frace^f^-1(x)+1e^f^-1(x)-1$. Now solve for $e^f^-1(x)$ first. To do this, multiply by the denominator. You get $x(e^f^-1(x)-1)=e^f^-1(x)+1$. Group the $e^f^-1(x)$ to get $(x-1)e^f^-1(x)=1+x$. Therefore $e^f^-1(x)=fracx+1x-1$. Finally, take natural logarithms on both sides: $f^-1(x)=lnleft(fracx+1x-1right)$.
    – spiralstotheleft
    yesterday










  • For (6.a) multiply and divide by $sqrtx+1-sqrtx$. For (6.b) use that $sin(2x)=2sin(x)cos(x)$, that $1-cos^2(x)=sin^2(x)$, and that $cot(x)=fraccos(x)sin(x)$. Everything simplifies.
    – spiralstotheleft
    yesterday












up vote
-4
down vote

favorite









up vote
-4
down vote

favorite











I'm having trouble with 4-6. The answers are on the next page of the PDF. I need to understand how they arrived at those answers.



Problems




trigonometry logarithms inverse-function




share|cite|improve this question











I'm having trouble with 4-6. The answers are on the next page of the PDF. I need to understand how they arrived at those answers.



Problems





trigonometry logarithms inverse-function





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked yesterday









user581750

6




6




put on hold as off-topic by Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Isaac Browne, amWhy, Arnaud Mortier, Simply Beautiful Art, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 3




    It's better to post one question at a time, write the problem out in the body of your question, and explain what you have tried, what you're stuck on, and what your thoughts are about it.
    – littleO
    yesterday






  • 1




    Welcome to Stackexchange. See here and here for more information on how to improve your post, as well as here and here for information on how to write math on this site.
    – Simply Beautiful Art
    yesterday










  • For (4) replace $x$ by $f^-1(x)$. You get $x=f(f^-1(x))=frace^f^-1(x)+1e^f^-1(x)-1$. Now solve for $e^f^-1(x)$ first. To do this, multiply by the denominator. You get $x(e^f^-1(x)-1)=e^f^-1(x)+1$. Group the $e^f^-1(x)$ to get $(x-1)e^f^-1(x)=1+x$. Therefore $e^f^-1(x)=fracx+1x-1$. Finally, take natural logarithms on both sides: $f^-1(x)=lnleft(fracx+1x-1right)$.
    – spiralstotheleft
    yesterday










  • For (6.a) multiply and divide by $sqrtx+1-sqrtx$. For (6.b) use that $sin(2x)=2sin(x)cos(x)$, that $1-cos^2(x)=sin^2(x)$, and that $cot(x)=fraccos(x)sin(x)$. Everything simplifies.
    – spiralstotheleft
    yesterday












  • 3




    It's better to post one question at a time, write the problem out in the body of your question, and explain what you have tried, what you're stuck on, and what your thoughts are about it.
    – littleO
    yesterday






  • 1




    Welcome to Stackexchange. See here and here for more information on how to improve your post, as well as here and here for information on how to write math on this site.
    – Simply Beautiful Art
    yesterday










  • For (4) replace $x$ by $f^-1(x)$. You get $x=f(f^-1(x))=frace^f^-1(x)+1e^f^-1(x)-1$. Now solve for $e^f^-1(x)$ first. To do this, multiply by the denominator. You get $x(e^f^-1(x)-1)=e^f^-1(x)+1$. Group the $e^f^-1(x)$ to get $(x-1)e^f^-1(x)=1+x$. Therefore $e^f^-1(x)=fracx+1x-1$. Finally, take natural logarithms on both sides: $f^-1(x)=lnleft(fracx+1x-1right)$.
    – spiralstotheleft
    yesterday










  • For (6.a) multiply and divide by $sqrtx+1-sqrtx$. For (6.b) use that $sin(2x)=2sin(x)cos(x)$, that $1-cos^2(x)=sin^2(x)$, and that $cot(x)=fraccos(x)sin(x)$. Everything simplifies.
    – spiralstotheleft
    yesterday







3




3




It's better to post one question at a time, write the problem out in the body of your question, and explain what you have tried, what you're stuck on, and what your thoughts are about it.
– littleO
yesterday




It's better to post one question at a time, write the problem out in the body of your question, and explain what you have tried, what you're stuck on, and what your thoughts are about it.
– littleO
yesterday




1




1




Welcome to Stackexchange. See here and here for more information on how to improve your post, as well as here and here for information on how to write math on this site.
– Simply Beautiful Art
yesterday




Welcome to Stackexchange. See here and here for more information on how to improve your post, as well as here and here for information on how to write math on this site.
– Simply Beautiful Art
yesterday












For (4) replace $x$ by $f^-1(x)$. You get $x=f(f^-1(x))=frace^f^-1(x)+1e^f^-1(x)-1$. Now solve for $e^f^-1(x)$ first. To do this, multiply by the denominator. You get $x(e^f^-1(x)-1)=e^f^-1(x)+1$. Group the $e^f^-1(x)$ to get $(x-1)e^f^-1(x)=1+x$. Therefore $e^f^-1(x)=fracx+1x-1$. Finally, take natural logarithms on both sides: $f^-1(x)=lnleft(fracx+1x-1right)$.
– spiralstotheleft
yesterday




For (4) replace $x$ by $f^-1(x)$. You get $x=f(f^-1(x))=frace^f^-1(x)+1e^f^-1(x)-1$. Now solve for $e^f^-1(x)$ first. To do this, multiply by the denominator. You get $x(e^f^-1(x)-1)=e^f^-1(x)+1$. Group the $e^f^-1(x)$ to get $(x-1)e^f^-1(x)=1+x$. Therefore $e^f^-1(x)=fracx+1x-1$. Finally, take natural logarithms on both sides: $f^-1(x)=lnleft(fracx+1x-1right)$.
– spiralstotheleft
yesterday












For (6.a) multiply and divide by $sqrtx+1-sqrtx$. For (6.b) use that $sin(2x)=2sin(x)cos(x)$, that $1-cos^2(x)=sin^2(x)$, and that $cot(x)=fraccos(x)sin(x)$. Everything simplifies.
– spiralstotheleft
yesterday




For (6.a) multiply and divide by $sqrtx+1-sqrtx$. For (6.b) use that $sin(2x)=2sin(x)cos(x)$, that $1-cos^2(x)=sin^2(x)$, and that $cot(x)=fraccos(x)sin(x)$. Everything simplifies.
– spiralstotheleft
yesterday















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