Question

How do I find the inverse and domain of f?
f^-1(x)

Answer 1

substitute the range with the domain of f to get the f^1

Answer 2

Range of \(f\) is the domain of \(f^{-1}\) and the domain of \(f\) is the range of \(f^{-1}\)

Answer 3

an example would be most helpful

Answer 4

so the domain of f^-1 would be (∞,∞) and the range would be the same correct? but would f^-1(x)=?

The problem is f(x)= In(x-3)

Answer 5

Since the domain for \(f(x) = \ln(x-3)\) is \((3, \infty)\) That would be the range of your inverse function.

The domain of the inverse is \((-\infty, \infty)\) however, so you were correct about that.

Answer 6

do you know the inverse of
\[\ln(x)\]?

Answer 7

I don't know what the inverse of f^-1(x)=

Answer 8

the inverse of
\[\ln(x)\] is
\[e^x\] and vice versa

Answer 9

so
\[e^{\ln(x)}=x\] and likewise
\[\ln(e^x)=x\]

Answer 10

if you want the inverse of
\[\ln(x-3)\] you can write
\[y=\ln(x-3)\] and solve for x
\[e^y=x-3\]
\[x=e^y+3\] so your inverse is
\[f^{-1}(x)=e^x+3\]

Answer 11

Thank you!