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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x^{2} - 4)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $4$ .

$f (5 x^{2} - 4) = 20 x^{2} + 4 \cdot - 4 - 3$

Multiply $4$ by $- 4$ .

$f (5 x^{2} - 4) = 20 x^{2} - 16 - 3$

Step 4

Subtract $3$ from $- 16$ .

$f (5 x^{2} - 4) = 20 x^{2} - 19$