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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (3 x^{3} - 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $4$ .

$f (3 x^{3} - 1) = 12 x^{3} + 4 \cdot - 1 - 1$

Multiply $4$ by $- 1$ .

$f (3 x^{3} - 1) = 12 x^{3} - 4 - 1$

Step 4

Subtract $1$ from $- 4$ .

$f (3 x^{3} - 1) = 12 x^{3} - 5$