Find g(f(x)) f(x)=18x^2-5x , g(x)=13x-10

$f (x) = 18 x^{2} - 5 x$ , $g (x) = 13 x - 10$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (18 x^{2} - 5 x)$ by substituting in the value of $f$ into $g$ .

$g (18 x^{2} - 5 x) = 13 (18 x^{2} - 5 x) - 10$

Step 3

Simplify each term.

Apply the distributive property.

$g (18 x^{2} - 5 x) = 13 (18 x^{2}) + 13 (- 5 x) - 10$

Multiply $18$ by $13$ .

$g (18 x^{2} - 5 x) = 234 x^{2} + 13 (- 5 x) - 10$

Multiply $- 5$ by $13$ .

$g (18 x^{2} - 5 x) = 234 x^{2} - 65 x - 10$