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Chapter 1: Problem 26

Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(f(x)=\sqrt{x+8}+2\) (a) \(f(-8)\) (b) \(f(1)\) (c) \(f(x-8)\)

Short Answer

Expert verified
The answer is \(f(-8) = 2\), \(f(1) = 5\), and \(f(x-8) = \sqrt{x} + 2\) (for \(x \geq 0\))

Step by step solution

01

Evaluate \(f(-8)\)

Substitute -8 into \(f(x) = \sqrt{x+8} + 2\). We have \(f(-8) = \sqrt{-8+8} + 2 = \sqrt{0} + 2 = 0 + 2 = 2\)
02

Evaluate \(f(1)\)

Substitute 1 into \(f(x) = \sqrt{x+8} + 2\). We have \(f(1) = \sqrt{1+8} + 2 = \sqrt{9} + 2 = 3 + 2 = 5\)
03

Evaluate \(f(x-8)\)

Substitute \(x-8\) into \(f(x) = \sqrt{x+8} + 2\). We have \(f(x-8) = \sqrt{(x-8)+8} + 2 = \sqrt{x} + 2\). It's important to note that this result is valid only for \(x \geq 0\), because of the square root operation.

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Most popular questions from this chapter

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