Find f(g(x)) f(x)=5x-1 and g(x)=4x^2-3

$f (x) = 5 x - 1$ and $g (x) = 4 x^{2} - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x^{2} - 3)$ by substituting in the value of $g$ into $f$ .

$f (4 x^{2} - 3) = 5 (4 x^{2} - 3) - 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (4 x^{2} - 3) = 5 (4 x^{2}) + 5 \cdot - 3 - 1$

Multiply $4$ by $5$ .

$f (4 x^{2} - 3) = 20 x^{2} + 5 \cdot - 3 - 1$

Multiply $5$ by $- 3$ .

$f (4 x^{2} - 3) = 20 x^{2} - 15 - 1$

Step 4

Subtract $1$ from $- 15$ .

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