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) $f(2) = \square$ (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 \( f(2)=\frac{6\times(2)^{2}-1}{(2)^{2}} \).

Step2: Calculate the numerator and denominator

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

Answer:

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