Find f(g(x)) f(x)=5x^2+5 ; g(x)=4x-2

$f (x) = 5 x^{2} + 5$ ; $g (x) = 4 x - 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify each term.

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

$f (4 x - 2) = 5 ((4 x - 2) (4 x - 2)) + 5$

Expand $(4 x - 2) (4 x - 2)$ using the FOIL Method.

Apply the distributive property.

$f (4 x - 2) = 5 (4 x (4 x - 2) - 2 (4 x - 2)) + 5$

Apply the distributive property.

$f (4 x - 2) = 5 (4 x (4 x) + 4 x \cdot - 2 - 2 (4 x - 2)) + 5$

Apply the distributive property.

$f (4 x - 2) = 5 (4 x (4 x) + 4 x \cdot - 2 - 2 (4 x) - 2 \cdot - 2) + 5$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (4 x - 2) = 5 (4 \cdot (4 x \cdot x) + 4 x \cdot - 2 - 2 (4 x) - 2 \cdot - 2) + 5$

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

Move $x$ .

$f (4 x - 2) = 5 (4 \cdot (4 (x \cdot x)) + 4 x \cdot - 2 - 2 (4 x) - 2 \cdot - 2) + 5$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$f (4 x - 2) = 5 (16 x^{2} + 4 x \cdot - 2 - 2 (4 x) - 2 \cdot - 2) + 5$

Multiply $- 2$ by $4$ .

$f (4 x - 2) = 5 (16 x^{2} - 8 x - 2 (4 x) - 2 \cdot - 2) + 5$

Multiply $4$ by $- 2$ .

$f (4 x - 2) = 5 (16 x^{2} - 8 x - 8 x - 2 \cdot - 2) + 5$

Multiply $- 2$ by $- 2$ .

$f (4 x - 2) = 5 (16 x^{2} - 8 x - 8 x + 4) + 5$

Subtract $8 x$ from $- 8 x$ .

$f (4 x - 2) = 5 (16 x^{2} - 16 x + 4) + 5$

Apply the distributive property.

$f (4 x - 2) = 5 (16 x^{2}) + 5 (- 16 x) + 5 \cdot 4 + 5$

Simplify.

Multiply $16$ by $5$ .

$f (4 x - 2) = 80 x^{2} + 5 (- 16 x) + 5 \cdot 4 + 5$

Multiply $- 16$ by $5$ .

$f (4 x - 2) = 80 x^{2} - 80 x + 5 \cdot 4 + 5$

Multiply $5$ by $4$ .

$f (4 x - 2) = 80 x^{2} - 80 x + 20 + 5$

Step 4

Add $20$ and $5$ .

$f (4 x - 2) = 80 x^{2} - 80 x + 25$

Find f(g(x)) f(x)=5x^2+5 ; g(x)=4x-2

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