Find f(g(x)) f(x)=x^2+2x+1 ; g(x)=10x-14

$f (x) = x^{2} + 2 x + 1$ ; $g (x) = 10 x - 14$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (10 x - 14)$ by substituting in the value of $g$ into $f$ .

$f (10 x - 14) = {(10 x - 14)}^{2} + 2 (10 x - 14) + 1$

Step 3

Simplify each term.

Rewrite ${(10 x - 14)}^{2}$ as $(10 x - 14) (10 x - 14)$ .

$f (10 x - 14) = (10 x - 14) (10 x - 14) + 2 (10 x - 14) + 1$

Expand $(10 x - 14) (10 x - 14)$ using the FOIL Method.

Apply the distributive property.

$f (10 x - 14) = 10 x (10 x - 14) - 14 (10 x - 14) + 2 (10 x - 14) + 1$

Apply the distributive property.

$f (10 x - 14) = 10 x (10 x) + 10 x \cdot - 14 - 14 (10 x - 14) + 2 (10 x - 14) + 1$

Apply the distributive property.

$f (10 x - 14) = 10 x (10 x) + 10 x \cdot - 14 - 14 (10 x) - 14 \cdot - 14 + 2 (10 x - 14) + 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (10 x - 14) = 10 \cdot (10 x \cdot x) + 10 x \cdot - 14 - 14 (10 x) - 14 \cdot - 14 + 2 (10 x - 14) + 1$

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

Move $x$ .

$f (10 x - 14) = 10 \cdot (10 (x \cdot x)) + 10 x \cdot - 14 - 14 (10 x) - 14 \cdot - 14 + 2 (10 x - 14) + 1$

Multiply $x$ by $x$ .

$f (10 x - 14) = 10 \cdot (10 x^{2}) + 10 x \cdot - 14 - 14 (10 x) - 14 \cdot - 14 + 2 (10 x - 14) + 1$

Multiply $10$ by $10$ .

$f (10 x - 14) = 100 x^{2} + 10 x \cdot - 14 - 14 (10 x) - 14 \cdot - 14 + 2 (10 x - 14) + 1$

Multiply $- 14$ by $10$ .

$f (10 x - 14) = 100 x^{2} - 140 x - 14 (10 x) - 14 \cdot - 14 + 2 (10 x - 14) + 1$

Multiply $10$ by $- 14$ .

$f (10 x - 14) = 100 x^{2} - 140 x - 140 x - 14 \cdot - 14 + 2 (10 x - 14) + 1$

Multiply $- 14$ by $- 14$ .

$f (10 x - 14) = 100 x^{2} - 140 x - 140 x + 196 + 2 (10 x - 14) + 1$

Subtract $140 x$ from $- 140 x$ .

$f (10 x - 14) = 100 x^{2} - 280 x + 196 + 2 (10 x - 14) + 1$

Apply the distributive property.

$f (10 x - 14) = 100 x^{2} - 280 x + 196 + 2 (10 x) + 2 \cdot - 14 + 1$

Multiply $10$ by $2$ .

$f (10 x - 14) = 100 x^{2} - 280 x + 196 + 20 x + 2 \cdot - 14 + 1$

Multiply $2$ by $- 14$ .

$f (10 x - 14) = 100 x^{2} - 280 x + 196 + 20 x - 28 + 1$

Step 4

Simplify by adding terms.

Add $- 280 x$ and $20 x$ .

$f (10 x - 14) = 100 x^{2} - 260 x + 196 - 28 + 1$

Simplify by adding and subtracting.

Subtract $28$ from $196$ .

$f (10 x - 14) = 100 x^{2} - 260 x + 168 + 1$

Add $168$ and $1$ .

$f (10 x - 14) = 100 x^{2} - 260 x + 169$

Find f(g(x)) f(x)=x^2+2x+1 ; g(x)=10x-14

Related Questions

Support LCMGCF.com by disabling your adblocker.