Problem preview

F-BF.4.a Warmup M2-017-A03-V02

Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.

Find the inverse of a square-root function by swapping x and y and solving

Problem

Derive the inverse of \(f(x)=\sqrt{x-3}\). Record the original domain and range, swap \(x\) and \(y\), solve the resulting radical equation by squaring, state the inverse domain and range, and check \(f^{-1}(f(7))\).

Answer choices

Choose your path.

Preview only

f⁻¹(x)=x²−3, for x≥0.

f⁻¹(x)=(x−3)², for x≥3.

f⁻¹(x)=x²+3, for all real x.

f⁻¹(x)=x²+3, for x≥0.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

Curriculum context

Course: Math II
Standard: F-BF.4.a
Category: Functions
Domain: Building Functions
Objective: Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.
Problem type: Find the inverse of a square-root function by swapping x and y and solving