Question

evaluate the function at the given values of the independent variable and simplify.
$f(x)=\frac{3x^{2}-1}{x^{2}}$
(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 $f(x)$

$f(2)=\frac{3(2)^2 - 1}{(2)^2}$

Step2: Calculate powers first

$f(2)=\frac{3(4) - 1}{4}$

Step3: Compute numerator

$f(2)=\frac{12 - 1}{4}=\frac{11}{4}$

Step1: Substitute $x=-2$ into $f(x)$

$f(-2)=\frac{3(-2)^2 - 1}{(-2)^2}$

Step2: Calculate powers first

$f(-2)=\frac{3(4) - 1}{4}$

Step3: Compute numerator

$f(-2)=\frac{12 - 1}{4}=\frac{11}{4}$

Step1: Substitute $x=-x$ into $f(x)$

$f(-x)=\frac{3(-x)^2 - 1}{(-x)^2}$

Step2: Simplify squared terms

$f(-x)=\frac{3x^2 - 1}{x^2}$

Answer:

(a) $\frac{11}{4}$
(b) $\frac{11}{4}$
(c) $\frac{3x^2 - 1}{x^2}$