Problem preview

F-BF.4.a Warmup M2-017-A03-V04

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 \(f(x)=3\sqrt{x-4}-2\). State the original domain and range, swap \(x\) and \(y\), isolate the radical in inverse-operation order, square and solve, then state the inverse domain and range and verify \(f^{-1}(f(13))\).

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f⁻¹(x)=[(x+2)/3]²+4, for x≥−2.

f⁻¹(x)=[(x+2)/3]²+4, for all real x.

f⁻¹(x)=−[(x+2)/3]²+4, for x≥−2.

f⁻¹(x)=[(x−2)/3]²−4, for x≥2.

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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