Problem

If $ f(x) = x^5 + x^3 + x $ , find $ f^{-1} (3) $…

01:15

Problem 15 Easy Difficulty

Assume that $ f $ is a one-to-one function.

(a) If $ f(6) = 17 $ , what is $ f^{-1} (17) $?
(a) If $ f^{-1} (3) = 2 $ , what is $ f(2) $?

Answer

a) $f^{-1}(17)=6$
b) $f(2)=3$

More Answers

01:14

Jeffrey P.

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

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Video Transcript

in this problem. We're talking about inverse functions and particularly coordinate pairs that would fall on inverse functions. And one of the features of inverse functions is that if F of X contains the point a B, then f inverse of X will contain the point B A. So the coordinates switch places a and B switch. So if you have the 0.6 17 as a point on f of X, you're going to have the 170.0.17 6 as a point on F in verse. So that tells us that F inverse of 17 will be six. Similarly, if you have the 0.32 on f inverse, you're going to have the 0.23 on F and so f of two will be three.

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Top Calculus 3 Educators

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Campbell University

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