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Chapter 2: Problem 1

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$ f(x)=4 x \text { and } g(x)=\frac{x}{4} $$

Short Answer

Expert verified
The compositions \(f(g(x)) = x\) and \(g(f(x)) = x \) show that the functions f and g are inverses of each other.

Step by step solution

01

Find \(f(g(x))\)

First, to find \(f(g(x))\), substitute \(g(x) = \frac{x}{4}\) into function \(f(x)\). Therefore, \(f(g(x)) = 4*(\frac{x}{4}) = x\).
02

Find \(g(f(x))\)

Next, to find \(g(f(x))\), substitute \(f(x) = 4x\) into function \(g(x)\). Therefore, \(g(f(x)) = \frac{(4x)}{4} = x\).
03

Determine if f and g are inverse of each other

Since \(f(g(x)) = x\) and \(g(f(x)) = x \), functions f and g are indeed inverses of each other.

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