Find f(g(x)) f(x)=5x-4 and g(x)=2x^2-3

$f (x) = 5 x - 4$ and $g (x) = 2 x^{2} - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x^{2} - 3)$ by substituting in the value of $g$ into $f$ .

$f (2 x^{2} - 3) = 5 (2 x^{2} - 3) - 4$

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $5$ .

$f (2 x^{2} - 3) = 10 x^{2} + 5 \cdot - 3 - 4$

Multiply $5$ by $- 3$ .

$f (2 x^{2} - 3) = 10 x^{2} - 15 - 4$

Step 4

Subtract $4$ from $- 15$ .

$f (2 x^{2} - 3) = 10 x^{2} - 19$