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Can't find solution derivative of inverse function problem!
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
I am completely stuck on this problem.
It reads:
If $g$ is the inverse function of $f(x) = 2x + ln(x)$ , find $g'(2)$.
I know that $g'(a) = 1 / f'( g(a) )$
I've tried this a whole bunch of ways. I can't find $g(x)$ and I tried to use the online inverse function calculators to find it and they don't have a solution either! This means I can't find $g(2)$.
My calculus book has given me several problems where I can't seem to find the inverse. So how am I supposed to use that formula?
My only other idea was to use linear algebra. As in find the tangent line at $(f(x), x)$ and reflect about $y = x$. But I still can't find $x$!
derivatives inverse-function
edited Jul 19 at 15:25
Green.H
1,046216
asked Jul 19 at 15:10
Dr. Snow
523
add a comment |Â
up vote
1
down vote
favorite
I am completely stuck on this problem.
It reads:
If $g$ is the inverse function of $f(x) = 2x + ln(x)$ , find $g'(2)$.
I know that $g'(a) = 1 / f'( g(a) )$
I've tried this a whole bunch of ways. I can't find $g(x)$ and I tried to use the online inverse function calculators to find it and they don't have a solution either! This means I can't find $g(2)$.
My calculus book has given me several problems where I can't seem to find the inverse. So how am I supposed to use that formula?
My only other idea was to use linear algebra. As in find the tangent line at $(f(x), x)$ and reflect about $y = x$. But I still can't find $x$!
derivatives inverse-function
edited Jul 19 at 15:25
Green.H
1,046216
asked Jul 19 at 15:10
Dr. Snow
523
Did you find what $f'(x)$ is? Most likely this problem isn't asking for the solution to $g(x)$ (it is not an elementary function), so just write your answer in terms of $g(x)$
– Dark Malthorp
Jul 19 at 15:12
3
I really think you can work out $g(2)$ on your own. Just try the first value you think of.
– lulu
Jul 19 at 15:13
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am completely stuck on this problem.
It reads:
If $g$ is the inverse function of $f(x) = 2x + ln(x)$ , find $g'(2)$.
I know that $g'(a) = 1 / f'( g(a) )$
I've tried this a whole bunch of ways. I can't find $g(x)$ and I tried to use the online inverse function calculators to find it and they don't have a solution either! This means I can't find $g(2)$.
My calculus book has given me several problems where I can't seem to find the inverse. So how am I supposed to use that formula?
My only other idea was to use linear algebra. As in find the tangent line at $(f(x), x)$ and reflect about $y = x$. But I still can't find $x$!
derivatives inverse-function
edited Jul 19 at 15:25
Green.H
1,046216
asked Jul 19 at 15:10
Dr. Snow
523
I am completely stuck on this problem.
It reads:
If $g$ is the inverse function of $f(x) = 2x + ln(x)$ , find $g'(2)$.
I know that $g'(a) = 1 / f'( g(a) )$
I've tried this a whole bunch of ways. I can't find $g(x)$ and I tried to use the online inverse function calculators to find it and they don't have a solution either! This means I can't find $g(2)$.
My calculus book has given me several problems where I can't seem to find the inverse. So how am I supposed to use that formula?
My only other idea was to use linear algebra. As in find the tangent line at $(f(x), x)$ and reflect about $y = x$. But I still can't find $x$!
derivatives inverse-function
edited Jul 19 at 15:25
Green.H
1,046216
asked Jul 19 at 15:10
Dr. Snow
523
edited Jul 19 at 15:25
Green.H
1,046216
edited Jul 19 at 15:25
Green.H
1,046216
edited Jul 19 at 15:25
Green.H
1,046216
1,046216
asked Jul 19 at 15:10
Dr. Snow
523
asked Jul 19 at 15:10
Dr. Snow
523
asked Jul 19 at 15:10
Dr. Snow
523
523
Did you find what $f'(x)$ is? Most likely this problem isn't asking for the solution to $g(x)$ (it is not an elementary function), so just write your answer in terms of $g(x)$
– Dark Malthorp
Jul 19 at 15:12
3
I really think you can work out $g(2)$ on your own. Just try the first value you think of.
– lulu
Jul 19 at 15:13
add a comment |Â
Did you find what $f'(x)$ is? Most likely this problem isn't asking for the solution to $g(x)$ (it is not an elementary function), so just write your answer in terms of $g(x)$
– Dark Malthorp
Jul 19 at 15:12
3
I really think you can work out $g(2)$ on your own. Just try the first value you think of.
– lulu
Jul 19 at 15:13
Did you find what $f'(x)$ is? Most likely this problem isn't asking for the solution to $g(x)$ (it is not an elementary function), so just write your answer in terms of $g(x)$
– Dark Malthorp
Jul 19 at 15:12
Did you find what $f'(x)$ is? Most likely this problem isn't asking for the solution to $g(x)$ (it is not an elementary function), so just write your answer in terms of $g(x)$
– Dark Malthorp
Jul 19 at 15:12
3
3
I really think you can work out $g(2)$ on your own. Just try the first value you think of.
– lulu
Jul 19 at 15:13
I really think you can work out $g(2)$ on your own. Just try the first value you think of.
– lulu
Jul 19 at 15:13
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Use the formula.
$$
g'(2)=frac1f'(g(2))
$$
Hopefully you can find what $f'$ is. To find $g(2)$, let $c=g(2)$ and since $g$ is the inverse of $f$, we have that
$$
2c+ln c=f(c)=2
$$
Clearly $c=1$ is a solution. To argue that it is unique observe that $f$ is strictly increasing.
answered Jul 19 at 15:17
Foobaz John
18.1k41245
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Use the formula.
$$
g'(2)=frac1f'(g(2))
$$
Hopefully you can find what $f'$ is. To find $g(2)$, let $c=g(2)$ and since $g$ is the inverse of $f$, we have that
$$
2c+ln c=f(c)=2
$$
Clearly $c=1$ is a solution. To argue that it is unique observe that $f$ is strictly increasing.
answered Jul 19 at 15:17
Foobaz John
18.1k41245
add a comment |Â
up vote
1
down vote
accepted
Use the formula.
$$
g'(2)=frac1f'(g(2))
$$
Hopefully you can find what $f'$ is. To find $g(2)$, let $c=g(2)$ and since $g$ is the inverse of $f$, we have that
$$
2c+ln c=f(c)=2
$$
Clearly $c=1$ is a solution. To argue that it is unique observe that $f$ is strictly increasing.
answered Jul 19 at 15:17
Foobaz John
18.1k41245
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Use the formula.
$$
g'(2)=frac1f'(g(2))
$$
Hopefully you can find what $f'$ is. To find $g(2)$, let $c=g(2)$ and since $g$ is the inverse of $f$, we have that
$$
2c+ln c=f(c)=2
$$
Clearly $c=1$ is a solution. To argue that it is unique observe that $f$ is strictly increasing.
answered Jul 19 at 15:17
Foobaz John
18.1k41245
Use the formula.
$$
g'(2)=frac1f'(g(2))
$$
Hopefully you can find what $f'$ is. To find $g(2)$, let $c=g(2)$ and since $g$ is the inverse of $f$, we have that
$$
2c+ln c=f(c)=2
$$
Clearly $c=1$ is a solution. To argue that it is unique observe that $f$ is strictly increasing.
answered Jul 19 at 15:17
Foobaz John
18.1k41245
answered Jul 19 at 15:17
Foobaz John
18.1k41245
answered Jul 19 at 15:17
Foobaz John
18.1k41245
answered Jul 19 at 15:17
Foobaz John
18.1k41245
18.1k41245
add a comment |Â
add a comment |Â
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Did you find what $f'(x)$ is? Most likely this problem isn't asking for the solution to $g(x)$ (it is not an elementary function), so just write your answer in terms of $g(x)$
– Dark Malthorp
Jul 19 at 15:12
3
I really think you can work out $g(2)$ on your own. Just try the first value you think of.
– lulu
Jul 19 at 15:13