Find f(g(x)) f(x)=17x^2-10x , g(x)=19x-10

$f (x) = 17 x^{2} - 10 x$ , $g (x) = 19 x - 10$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (19 x - 10)$ by substituting in the value of $g$ into $f$ .

$f (19 x - 10) = 17 {(19 x - 10)}^{2} - 10 (19 x - 10)$

Step 3

Simplify each term.

Rewrite ${(19 x - 10)}^{2}$ as $(19 x - 10) (19 x - 10)$ .

$f (19 x - 10) = 17 ((19 x - 10) (19 x - 10)) - 10 (19 x - 10)$

Expand $(19 x - 10) (19 x - 10)$ using the FOIL Method.

Apply the distributive property.

$f (19 x - 10) = 17 (19 x (19 x - 10) - 10 (19 x - 10)) - 10 (19 x - 10)$

Apply the distributive property.

$f (19 x - 10) = 17 (19 x (19 x) + 19 x \cdot - 10 - 10 (19 x - 10)) - 10 (19 x - 10)$

Apply the distributive property.

$f (19 x - 10) = 17 (19 x (19 x) + 19 x \cdot - 10 - 10 (19 x) - 10 \cdot - 10) - 10 (19 x - 10)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (19 x - 10) = 17 (19 \cdot (19 x \cdot x) + 19 x \cdot - 10 - 10 (19 x) - 10 \cdot - 10) - 10 (19 x - 10)$

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

Move $x$ .

$f (19 x - 10) = 17 (19 \cdot (19 (x \cdot x)) + 19 x \cdot - 10 - 10 (19 x) - 10 \cdot - 10) - 10 (19 x - 10)$

Multiply $x$ by $x$ .

$f (19 x - 10) = 17 (19 \cdot (19 x^{2}) + 19 x \cdot - 10 - 10 (19 x) - 10 \cdot - 10) - 10 (19 x - 10)$

Multiply $19$ by $19$ .

$f (19 x - 10) = 17 (361 x^{2} + 19 x \cdot - 10 - 10 (19 x) - 10 \cdot - 10) - 10 (19 x - 10)$

Multiply $- 10$ by $19$ .

$f (19 x - 10) = 17 (361 x^{2} - 190 x - 10 (19 x) - 10 \cdot - 10) - 10 (19 x - 10)$

Multiply $19$ by $- 10$ .

$f (19 x - 10) = 17 (361 x^{2} - 190 x - 190 x - 10 \cdot - 10) - 10 (19 x - 10)$

Multiply $- 10$ by $- 10$ .

$f (19 x - 10) = 17 (361 x^{2} - 190 x - 190 x + 100) - 10 (19 x - 10)$

Subtract $190 x$ from $- 190 x$ .

$f (19 x - 10) = 17 (361 x^{2} - 380 x + 100) - 10 (19 x - 10)$

Apply the distributive property.

$f (19 x - 10) = 17 (361 x^{2}) + 17 (- 380 x) + 17 \cdot 100 - 10 (19 x - 10)$

Simplify.

Multiply $361$ by $17$ .

$f (19 x - 10) = 6137 x^{2} + 17 (- 380 x) + 17 \cdot 100 - 10 (19 x - 10)$

Multiply $- 380$ by $17$ .

$f (19 x - 10) = 6137 x^{2} - 6460 x + 17 \cdot 100 - 10 (19 x - 10)$

Multiply $17$ by $100$ .

$f (19 x - 10) = 6137 x^{2} - 6460 x + 1700 - 10 (19 x - 10)$

Apply the distributive property.

$f (19 x - 10) = 6137 x^{2} - 6460 x + 1700 - 10 (19 x) - 10 \cdot - 10$

Multiply $19$ by $- 10$ .

$f (19 x - 10) = 6137 x^{2} - 6460 x + 1700 - 190 x - 10 \cdot - 10$

Multiply $- 10$ by $- 10$ .

$f (19 x - 10) = 6137 x^{2} - 6460 x + 1700 - 190 x + 100$

Step 4

Simplify by adding terms.

Subtract $190 x$ from $- 6460 x$ .

$f (19 x - 10) = 6137 x^{2} - 6650 x + 1700 + 100$

Add $1700$ and $100$ .

$f (19 x - 10) = 6137 x^{2} - 6650 x + 1800$

Find f(g(x)) f(x)=17x^2-10x , g(x)=19x-10

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