Find f(g(x)) f(x)=5x-3 and g(x)=2x^2-5

$f (x) = 5 x - 3$ and $g (x) = 2 x^{2} - 5$

Set up the composite result function.

$f (g (x))$

Evaluate $f (2 x^{2} - 5)$ by substituting in the value of $g$ into $f$ .

$f (2 x^{2} - 5) = 5 (2 x^{2} - 5) - 3$

Simplify each term.

Apply the distributive property.

$f (2 x^{2} - 5) = 5 (2 x^{2}) + 5 \cdot - 5 - 3$

Multiply $2$ by $5$ .

$f (2 x^{2} - 5) = 10 x^{2} + 5 \cdot - 5 - 3$

Multiply $5$ by $- 5$ .

$f (2 x^{2} - 5) = 10 x^{2} - 25 - 3$

Subtract $3$ from $- 25$ .

$f (2 x^{2} - 5) = 10 x^{2} - 28$