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Chapter 8: Problem 30

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 simplified expression for \(f(-x) - f(x)\) given the function \(f(x) = x^{2} - 3x + 7\) is \(6x\).

Step by step solution

01

Find \(f(-x)\)

First, plug \(-x\) in the place of \(x\) in the original function. This gives the equation for \(f(-x)\) as \((-x)^{2} - 3(-x) + 7\). Simplify this equation to \(x^{2} + 3x + 7\).
02

Subtract \(f(x)\) from \(f(-x)\)

Next, subtract \(f(x)\) from \(f(-x)\). This gives \(f(-x) - f(x) = (x^{2} + 3x + 7) - (x^{2} - 3x + 7)\).
03

Simplify the expression

Simplify the above equation to produce the final answer. After distributing the negative sign and combining like terms, we get \(f(-x) - f(x) = 6x\).

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