Problem preview

F-BF.4.a Warmup M2-017-A04-V04

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

Find an inverse expression for a simple exponential function

Problem

Derive the inverse of \(f(x)=4\cdot~3^x\). Exchange \(x\) and \(y\) after stating the original domain and range, isolate \(3^y\), convert to a base-\(3\) logarithm, give the inverse domain and range, and verify \(f^{-1}(36)\).

Answer choices

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f⁻¹(x)=log₃(x/4), for x>0.

f⁻¹(x)=log₁₀(x/4), for x>0.

f⁻¹(x)=log₃(x)/4, for x>0.

f⁻¹(x)=log₃(x/4), for all real x.

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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 an inverse expression for a simple exponential function