Find f(g(x)) f(x)=5x^2+2x-5 , g(x)=7x+8 , h(x)=4x^2-10

$f (x) = 5 x^{2} + 2 x - 5$ , $g (x) = 7 x + 8$ , $h (x) = 4 x^{2} - 10$

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 $f$ .

$f (7 x + 8) = 5 {(7 x + 8)}^{2} + 2 (7 x + 8) - 5$

Step 3

Simplify each term.

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

$f (7 x + 8) = 5 ((7 x + 8) (7 x + 8)) + 2 (7 x + 8) - 5$

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

Apply the distributive property.

$f (7 x + 8) = 5 (7 x (7 x + 8) + 8 (7 x + 8)) + 2 (7 x + 8) - 5$

Apply the distributive property.

$f (7 x + 8) = 5 (7 x (7 x) + 7 x \cdot 8 + 8 (7 x + 8)) + 2 (7 x + 8) - 5$

Apply the distributive property.

$f (7 x + 8) = 5 (7 x (7 x) + 7 x \cdot 8 + 8 (7 x) + 8 \cdot 8) + 2 (7 x + 8) - 5$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (7 x + 8) = 5 (7 \cdot (7 x \cdot x) + 7 x \cdot 8 + 8 (7 x) + 8 \cdot 8) + 2 (7 x + 8) - 5$

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

Move $x$ .

$f (7 x + 8) = 5 (7 \cdot (7 (x \cdot x)) + 7 x \cdot 8 + 8 (7 x) + 8 \cdot 8) + 2 (7 x + 8) - 5$

Multiply $x$ by $x$ .

$f (7 x + 8) = 5 (7 \cdot (7 x^{2}) + 7 x \cdot 8 + 8 (7 x) + 8 \cdot 8) + 2 (7 x + 8) - 5$

Multiply $7$ by $7$ .

$f (7 x + 8) = 5 (49 x^{2} + 7 x \cdot 8 + 8 (7 x) + 8 \cdot 8) + 2 (7 x + 8) - 5$

Multiply $8$ by $7$ .

$f (7 x + 8) = 5 (49 x^{2} + 56 x + 8 (7 x) + 8 \cdot 8) + 2 (7 x + 8) - 5$

Multiply $7$ by $8$ .

$f (7 x + 8) = 5 (49 x^{2} + 56 x + 56 x + 8 \cdot 8) + 2 (7 x + 8) - 5$

Multiply $8$ by $8$ .

$f (7 x + 8) = 5 (49 x^{2} + 56 x + 56 x + 64) + 2 (7 x + 8) - 5$

Add $56 x$ and $56 x$ .

$f (7 x + 8) = 5 (49 x^{2} + 112 x + 64) + 2 (7 x + 8) - 5$

Apply the distributive property.

$f (7 x + 8) = 5 (49 x^{2}) + 5 (112 x) + 5 \cdot 64 + 2 (7 x + 8) - 5$

Simplify.

Multiply $49$ by $5$ .

$f (7 x + 8) = 245 x^{2} + 5 (112 x) + 5 \cdot 64 + 2 (7 x + 8) - 5$

Multiply $112$ by $5$ .

$f (7 x + 8) = 245 x^{2} + 560 x + 5 \cdot 64 + 2 (7 x + 8) - 5$

Multiply $5$ by $64$ .

$f (7 x + 8) = 245 x^{2} + 560 x + 320 + 2 (7 x + 8) - 5$

Apply the distributive property.

$f (7 x + 8) = 245 x^{2} + 560 x + 320 + 2 (7 x) + 2 \cdot 8 - 5$

Multiply $7$ by $2$ .

$f (7 x + 8) = 245 x^{2} + 560 x + 320 + 14 x + 2 \cdot 8 - 5$

Multiply $2$ by $8$ .

$f (7 x + 8) = 245 x^{2} + 560 x + 320 + 14 x + 16 - 5$

Step 4

Simplify by adding terms.

Add $560 x$ and $14 x$ .

$f (7 x + 8) = 245 x^{2} + 574 x + 320 + 16 - 5$

Simplify by adding and subtracting.

Add $320$ and $16$ .

$f (7 x + 8) = 245 x^{2} + 574 x + 336 - 5$

Subtract $5$ from $336$ .

$f (7 x + 8) = 245 x^{2} + 574 x + 331$

Find f(g(x)) f(x)=5x^2+2x-5 , g(x)=7x+8 , h(x)=4x^2-10

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