Find g(f(x)) f(x)=6x-4 g(x)=3x^2-2x-10

$f (x) = 6 x - 4$ $g (x) = 3 x^{2} - 2 x - 10$

Set up the composite result function.

$g (f (x))$

Evaluate $g (6 x - 4)$ by substituting in the value of $f$ into $g$ .

$g (6 x - 4) = 3 {(6 x - 4)}^{2} - 2 (6 x - 4) - 10$

Simplify each term.

Rewrite ${(6 x - 4)}^{2}$ as $(6 x - 4) (6 x - 4)$ .

$g (6 x - 4) = 3 ((6 x - 4) (6 x - 4)) - 2 (6 x - 4) - 10$

Expand $(6 x - 4) (6 x - 4)$ using the FOIL Method.

Apply the distributive property.

$g (6 x - 4) = 3 (6 x (6 x - 4) - 4 (6 x - 4)) - 2 (6 x - 4) - 10$

Apply the distributive property.

$g (6 x - 4) = 3 (6 x (6 x) + 6 x \cdot - 4 - 4 (6 x - 4)) - 2 (6 x - 4) - 10$

Apply the distributive property.

$g (6 x - 4) = 3 (6 x (6 x) + 6 x \cdot - 4 - 4 (6 x) - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$g (6 x - 4) = 3 (6 \cdot (6 x \cdot x) + 6 x \cdot - 4 - 4 (6 x) - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$g (6 x - 4) = 3 (6 \cdot (6 (x \cdot x)) + 6 x \cdot - 4 - 4 (6 x) - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Multiply $x$ by $x$ .

$g (6 x - 4) = 3 (6 \cdot (6 x^{2}) + 6 x \cdot - 4 - 4 (6 x) - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Multiply $6$ by $6$ .

$g (6 x - 4) = 3 (36 x^{2} + 6 x \cdot - 4 - 4 (6 x) - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Multiply $- 4$ by $6$ .

$g (6 x - 4) = 3 (36 x^{2} - 24 x - 4 (6 x) - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Multiply $6$ by $- 4$ .

$g (6 x - 4) = 3 (36 x^{2} - 24 x - 24 x - 4 \cdot - 4) - 2 (6 x - 4) - 10$

Multiply $- 4$ by $- 4$ .

$g (6 x - 4) = 3 (36 x^{2} - 24 x - 24 x + 16) - 2 (6 x - 4) - 10$

Subtract $24 x$ from $- 24 x$ .

$g (6 x - 4) = 3 (36 x^{2} - 48 x + 16) - 2 (6 x - 4) - 10$

Apply the distributive property.

$g (6 x - 4) = 3 (36 x^{2}) + 3 (- 48 x) + 3 \cdot 16 - 2 (6 x - 4) - 10$

Simplify.

Multiply $36$ by $3$ .

$g (6 x - 4) = 108 x^{2} + 3 (- 48 x) + 3 \cdot 16 - 2 (6 x - 4) - 10$

Multiply $- 48$ by $3$ .

$g (6 x - 4) = 108 x^{2} - 144 x + 3 \cdot 16 - 2 (6 x - 4) - 10$

Multiply $3$ by $16$ .

$g (6 x - 4) = 108 x^{2} - 144 x + 48 - 2 (6 x - 4) - 10$

Apply the distributive property.

$g (6 x - 4) = 108 x^{2} - 144 x + 48 - 2 (6 x) - 2 \cdot - 4 - 10$

Multiply $6$ by $- 2$ .

$g (6 x - 4) = 108 x^{2} - 144 x + 48 - 12 x - 2 \cdot - 4 - 10$

Multiply $- 2$ by $- 4$ .

$g (6 x - 4) = 108 x^{2} - 144 x + 48 - 12 x + 8 - 10$

Simplify by adding terms.

Subtract $12 x$ from $- 144 x$ .

$g (6 x - 4) = 108 x^{2} - 156 x + 48 + 8 - 10$

Simplify by adding and subtracting.

Add $48$ and $8$ .

$g (6 x - 4) = 108 x^{2} - 156 x + 56 - 10$

Subtract $10$ from $56$ .

$g (6 x - 4) = 108 x^{2} - 156 x + 46$

Find g(f(x)) f(x)=6x-4 g(x)=3x^2-2x-10

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