Evaluate the Function f(2)=(3x^2-7)/(4x^2-3)

$f (2) = \frac{3 x^{2} - 7}{4 x^{2} - 3}$

Replace the variable $x$ with $2$ in the expression.

$f (2) = \frac{3 {(2)}^{2} - 7}{4 {(2)}^{2} - 3}$

Simplify the result.

Simplify the numerator.

Raise $2$ to the power of $2$ .

$f (2) = \frac{3 \cdot 4 - 7}{4 \cdot 2^{2} - 3}$

Multiply $3$ by $4$ .

$f (2) = \frac{12 - 7}{4 \cdot 2^{2} - 3}$

Subtract $7$ from $12$ .

$f (2) = \frac{5}{4 \cdot 2^{2} - 3}$

Simplify the denominator.

Raise $2$ to the power of $2$ .

$f (2) = \frac{5}{4 \cdot 4 - 3}$

Multiply $4$ by $4$ .

$f (2) = \frac{5}{16 - 3}$

Subtract $3$ from $16$ .

$f (2) = \frac{5}{13}$

The final answer is $\frac{5}{13}$ .

$\frac{5}{13}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{13}$

Decimal Form:

$0.\overline{384615}$