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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Simplify each term.

Rewrite ${(4 x - 3)}^{2}$ as $(4 x - 3) (4 x - 3)$ .

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

Expand $(4 x - 3) (4 x - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

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

Multiply $- 3$ by $4$ .

$g (4 x - 3) = 3 (16 x^{2} - 12 x - 3 (4 x) - 3 \cdot - 3) - 2$

Multiply $4$ by $- 3$ .

$g (4 x - 3) = 3 (16 x^{2} - 12 x - 12 x - 3 \cdot - 3) - 2$

Multiply $- 3$ by $- 3$ .

$g (4 x - 3) = 3 (16 x^{2} - 12 x - 12 x + 9) - 2$

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

$g (4 x - 3) = 3 (16 x^{2} - 24 x + 9) - 2$

Apply the distributive property.

$g (4 x - 3) = 3 (16 x^{2}) + 3 (- 24 x) + 3 \cdot 9 - 2$

Simplify.

Multiply $16$ by $3$ .

$g (4 x - 3) = 48 x^{2} + 3 (- 24 x) + 3 \cdot 9 - 2$

Multiply $- 24$ by $3$ .

$g (4 x - 3) = 48 x^{2} - 72 x + 3 \cdot 9 - 2$

Multiply $3$ by $9$ .

$g (4 x - 3) = 48 x^{2} - 72 x + 27 - 2$

Step 4

Subtract $2$ from $27$ .

$g (4 x - 3) = 48 x^{2} - 72 x + 25$

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

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