## Related questions with answers

Question

Each Exercise gives a formula for a function y = f(x). In each case, find $f^{-1}(x)$ and identify the domain and range of $f^{-1}.$ As a check, show that $f\left(f^{-1}(x)\right)=f^{-1}(f(x))=x.$ $f(x)=1 / x^{2}, \quad x>0$

Solutions

VerifiedSolution A

Solution B

Answered 11 months ago

Step 1

1 of 7The goal of the exercise is to find the inverse of the function $f$ which is defined as

$f(x)=\frac{1}{x^2}$

for $x>0$ and to find the domain and the range of the function $f^{-1}$. Then we have to verify that $f[f^{-1}(x)]=f^{-1}[f(x)]=x$.

*Do you remember the inverse of a function?*

Answered 2 years ago

Step 1

1 of 5We have to find the formula of $f^{-1}(x)$ for $f(x) = \dfrac{1}{x^2}$.

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