Question

evaluate the function at the given values of the independent variable and simplify.
$f(x)=\frac{6x^2 - 1}{x^2}$
(a) $f(2)$ (b) $f(-2)$ (c) $f(-x)$
(a) $f(2)=\frac{23}{4}$ (type an integer or a fraction. simplify your answer.)
(b) $f(-2)=\square$ (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Substitute \( x = -2 \) into the function

We have the function \( f(x)=\frac{6x^{2}-1}{x^{2}} \). Substitute \( x = -2 \) into it, so we get \( f(-2)=\frac{6(-2)^{2}-1}{(-2)^{2}} \).

Step2: Calculate the numerator and denominator

First, calculate the exponent: \( (-2)^{2}=4 \). Then the numerator: \( 6\times4 - 1=24 - 1 = 23 \), and the denominator is \( 4 \). So \( f(-2)=\frac{23}{4} \).

Answer:

\(\frac{23}{4}\)