Find f(g(x)) f(x)=14x^2-10x , g(x)=7x-8

$f (x) = 14 x^{2} - 10 x$ , $g (x) = 7 x - 8$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (7 x - 8)$ by substituting in the value of $g$ into $f$ .

$f (7 x - 8) = 14 {(7 x - 8)}^{2} - 10 (7 x - 8)$

Step 3

Simplify each term.

Rewrite ${(7 x - 8)}^{2}$ as $(7 x - 8) (7 x - 8)$ .

$f (7 x - 8) = 14 ((7 x - 8) (7 x - 8)) - 10 (7 x - 8)$

Expand $(7 x - 8) (7 x - 8)$ using the FOIL Method.

Apply the distributive property.

$f (7 x - 8) = 14 (7 x (7 x - 8) - 8 (7 x - 8)) - 10 (7 x - 8)$

Apply the distributive property.

$f (7 x - 8) = 14 (7 x (7 x) + 7 x \cdot - 8 - 8 (7 x - 8)) - 10 (7 x - 8)$

Apply the distributive property.

$f (7 x - 8) = 14 (7 x (7 x) + 7 x \cdot - 8 - 8 (7 x) - 8 \cdot - 8) - 10 (7 x - 8)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (7 x - 8) = 14 (7 \cdot (7 x \cdot x) + 7 x \cdot - 8 - 8 (7 x) - 8 \cdot - 8) - 10 (7 x - 8)$

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

Move $x$ .

$f (7 x - 8) = 14 (7 \cdot (7 (x \cdot x)) + 7 x \cdot - 8 - 8 (7 x) - 8 \cdot - 8) - 10 (7 x - 8)$

Multiply $x$ by $x$ .

$f (7 x - 8) = 14 (7 \cdot (7 x^{2}) + 7 x \cdot - 8 - 8 (7 x) - 8 \cdot - 8) - 10 (7 x - 8)$

Multiply $7$ by $7$ .

$f (7 x - 8) = 14 (49 x^{2} + 7 x \cdot - 8 - 8 (7 x) - 8 \cdot - 8) - 10 (7 x - 8)$

Multiply $- 8$ by $7$ .

$f (7 x - 8) = 14 (49 x^{2} - 56 x - 8 (7 x) - 8 \cdot - 8) - 10 (7 x - 8)$

Multiply $7$ by $- 8$ .

$f (7 x - 8) = 14 (49 x^{2} - 56 x - 56 x - 8 \cdot - 8) - 10 (7 x - 8)$

Multiply $- 8$ by $- 8$ .

$f (7 x - 8) = 14 (49 x^{2} - 56 x - 56 x + 64) - 10 (7 x - 8)$

Subtract $56 x$ from $- 56 x$ .

$f (7 x - 8) = 14 (49 x^{2} - 112 x + 64) - 10 (7 x - 8)$

Apply the distributive property.

$f (7 x - 8) = 14 (49 x^{2}) + 14 (- 112 x) + 14 \cdot 64 - 10 (7 x - 8)$

Simplify.

Multiply $49$ by $14$ .

$f (7 x - 8) = 686 x^{2} + 14 (- 112 x) + 14 \cdot 64 - 10 (7 x - 8)$

Multiply $- 112$ by $14$ .

$f (7 x - 8) = 686 x^{2} - 1568 x + 14 \cdot 64 - 10 (7 x - 8)$

Multiply $14$ by $64$ .

$f (7 x - 8) = 686 x^{2} - 1568 x + 896 - 10 (7 x - 8)$

Apply the distributive property.

$f (7 x - 8) = 686 x^{2} - 1568 x + 896 - 10 (7 x) - 10 \cdot - 8$

Multiply $7$ by $- 10$ .

$f (7 x - 8) = 686 x^{2} - 1568 x + 896 - 70 x - 10 \cdot - 8$

Multiply $- 10$ by $- 8$ .

$f (7 x - 8) = 686 x^{2} - 1568 x + 896 - 70 x + 80$

Step 4

Simplify by adding terms.

Subtract $70 x$ from $- 1568 x$ .

$f (7 x - 8) = 686 x^{2} - 1638 x + 896 + 80$

Add $896$ and $80$ .

$f (7 x - 8) = 686 x^{2} - 1638 x + 976$

Find f(g(x)) f(x)=14x^2-10x , g(x)=7x-8

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