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Chapter 1: Problem 30

Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(f(x)=|x|+4\) (a) \(f(2)\) (b) \(f(-2)\) (c) \(f\left(x^{2}\right)\)

Short Answer

Expert verified
The results for the different inputs into the function are: (a) \(f(2)=6\), (b) \(f(-2)=6\), and (c) \(f(x^2)=x^2+4\)

Step by step solution

01

Substituting \(x=2\)

For (a), substitute \(x=2\) into the equation. Hence, \(f(2)=|2|+4\). The absolute value of 2 equals 2, so the function becomes \(f(2)=2+4\).
02

Substituting \(x=-2\)

For (b), substitute \(x=-2\) into the equation. Thus, \(f(-2)=|-2|+4\). The absolute value of -2 equals 2, hence the function becomes \(f(-2)=2+4\).
03

Substituting \(x=x^2\)

For (c), substitute \(x=x^2\) into the equation. Subsequently, \(f(x^2)=|x^2|+4\). Since \(x^2\) is always non-negative for real numbers x, the absolute value of \(x^2\) simply becomes \(x^2\). Therefore, the function becomes \(f(x^2)=x^2+4\).

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