## Related questions with answers

Question

Calculate $f^{-1}$(x) and state the domain and range of $f^{-1}$. $f(x)=\sqrt{x-2}$, a=2

Solutions

VerifiedSolution A

Solution B

Answered 1 year ago

Step 1

1 of 6We are asked to find the inverse of the function $f(x)=\sqrt{x-2}$. So, let us recall the steps in finding the inverse function given the one-to-one function.

Step 1

1 of 3From $f(x) = \sqrt{x-2}$ we write it with $y$

$\begin{align*} y &= \sqrt{x-2} \end{align*}$

Solve for $x$

$\begin{align*} y^2 &= x- 2 \\\\ y^2 + 2 &= x \\\\ x &= y^2 + 2 \end{align*}$

Swap $x$ and $y$, so that we can express the inverse as a function of $x$.

$\begin{align*} y &= x^2 + 2 \\\\ f^{-1} (x) &= x^2 + 2 \end{align*}$

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