Find f(g(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.

$f (g (x))$

Step 2

Evaluate $f (13 x - 10)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Rewrite ${(13 x - 10)}^{2}$ as $(13 x - 10) (13 x - 10)$ .

$f (13 x - 10) = 18 ((13 x - 10) (13 x - 10)) - 5 (13 x - 10)$

Expand $(13 x - 10) (13 x - 10)$ using the FOIL Method.

Apply the distributive property.

$f (13 x - 10) = 18 (13 x (13 x - 10) - 10 (13 x - 10)) - 5 (13 x - 10)$

Apply the distributive property.

$f (13 x - 10) = 18 (13 x (13 x) + 13 x \cdot - 10 - 10 (13 x - 10)) - 5 (13 x - 10)$

Apply the distributive property.

$f (13 x - 10) = 18 (13 x (13 x) + 13 x \cdot - 10 - 10 (13 x) - 10 \cdot - 10) - 5 (13 x - 10)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (13 x - 10) = 18 (13 \cdot (13 x \cdot x) + 13 x \cdot - 10 - 10 (13 x) - 10 \cdot - 10) - 5 (13 x - 10)$

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

Move $x$ .

$f (13 x - 10) = 18 (13 \cdot (13 (x \cdot x)) + 13 x \cdot - 10 - 10 (13 x) - 10 \cdot - 10) - 5 (13 x - 10)$

Multiply $x$ by $x$ .

$f (13 x - 10) = 18 (13 \cdot (13 x^{2}) + 13 x \cdot - 10 - 10 (13 x) - 10 \cdot - 10) - 5 (13 x - 10)$

Multiply $13$ by $13$ .

$f (13 x - 10) = 18 (169 x^{2} + 13 x \cdot - 10 - 10 (13 x) - 10 \cdot - 10) - 5 (13 x - 10)$

Multiply $- 10$ by $13$ .

$f (13 x - 10) = 18 (169 x^{2} - 130 x - 10 (13 x) - 10 \cdot - 10) - 5 (13 x - 10)$

Multiply $13$ by $- 10$ .

$f (13 x - 10) = 18 (169 x^{2} - 130 x - 130 x - 10 \cdot - 10) - 5 (13 x - 10)$

Multiply $- 10$ by $- 10$ .

$f (13 x - 10) = 18 (169 x^{2} - 130 x - 130 x + 100) - 5 (13 x - 10)$

Subtract $130 x$ from $- 130 x$ .

$f (13 x - 10) = 18 (169 x^{2} - 260 x + 100) - 5 (13 x - 10)$

Apply the distributive property.

$f (13 x - 10) = 18 (169 x^{2}) + 18 (- 260 x) + 18 \cdot 100 - 5 (13 x - 10)$

Simplify.

Multiply $169$ by $18$ .

$f (13 x - 10) = 3042 x^{2} + 18 (- 260 x) + 18 \cdot 100 - 5 (13 x - 10)$

Multiply $- 260$ by $18$ .

$f (13 x - 10) = 3042 x^{2} - 4680 x + 18 \cdot 100 - 5 (13 x - 10)$

Multiply $18$ by $100$ .

$f (13 x - 10) = 3042 x^{2} - 4680 x + 1800 - 5 (13 x - 10)$

Apply the distributive property.

$f (13 x - 10) = 3042 x^{2} - 4680 x + 1800 - 5 (13 x) - 5 \cdot - 10$

Multiply $13$ by $- 5$ .

$f (13 x - 10) = 3042 x^{2} - 4680 x + 1800 - 65 x - 5 \cdot - 10$

Multiply $- 5$ by $- 10$ .

$f (13 x - 10) = 3042 x^{2} - 4680 x + 1800 - 65 x + 50$

Step 4

Simplify by adding terms.

Subtract $65 x$ from $- 4680 x$ .

$f (13 x - 10) = 3042 x^{2} - 4745 x + 1800 + 50$

Add $1800$ and $50$ .

$f (13 x - 10) = 3042 x^{2} - 4745 x + 1850$

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

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