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F-BF.4.a Warmup M2-017-A07-V03

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

Choose a domain restriction so a quadratic has an inverse function

Problem

Use the vertex of \(f(x)=-(x+4)^{2}+1\) to define its complete right-branch domain. State the restriction and range, explain why the branch is decreasing and one-to-one, and relate the range to the inverse's domain.

Full quadratic with vertex split without the worked conclusion. Open full size
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Four variants of this problem type
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
Choose a domain restriction so a quadratic has an inverse function