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Chapter 1: Problem 98

Find \(f(-x)-f(x)\) for the given function \(f\) Then simplify the expression. $$f(x)=x^{2}-3 x+7$$

Short Answer

Expert verified
The final result for \(f(-x) - f(x)\) is \(6x\)

Step by step solution

01

Compute \(f(-x)\)

To compute \(f(-x)\), replace each instance of \(x\) in the given function with \(-x\). The resultant function becomes \(f(-x)= (-x)^{2}-3(-x)+7\)
02

Simplify \(f(-x)\)

Simplify the above equation to get \(f(-x) = x^{2}+3x+7\)
03

Compute \(f(-x)-f(x)\)

Subtract \(f(x)\) from \(f(-x)\). That is calculate \(f(-x)-f(x) = (x^{2}+3x+7) - (x^{2}-3x+7)\)
04

Simplify the Expression

By simplifying \(f(-x)-f(x)\), the result will be \(6x\)

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