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Chapter 1: Problem 6

What is the value of \(f(-2)\) if \(f(x)=\frac{x^2+4 x-8}{x-2}\) ? A) \(-3\) B) \(-1\) C) 1 D) 3

Short Answer

Expert verified
D) 3

Step by step solution

01

Substitute x with -2

First, we need to replace x with -2 in the function. The function is given as: \(f(x) = \frac{x^2 + 4x - 8}{x - 2}\). So, plugging -2 into the function, we get: \[f(-2) = \frac{(-2)^2 + 4(-2) - 8}{(-2) - 2}\] Step 2: Simplify the expression
02

Simplify the expression

Now let's simplify the expression. In the numerator, we have: \((-2)^2 = 4\), \(4(-2) = -8\), and \(4 - 8 - 8 = -12\). In the denominator, we have: \((-2) - 2 = -4\). So we get: \[f(-2) = \frac{-12}{-4}\] Step 3: Final simplification and find the value
03

Final simplification and find the value

Finally, let's simplify the expression by dividing -12 by -4 and find the value of f(-2). \[f(-2) = \frac{-12}{-4} = 3\] So, the value of f(-2) = 3. The correct answer is D) 3.

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