Find f(g(x)) f(x)=x^2-5 , g(x)=2x-7

$f (x) = x^{2} - 5$ , $g (x) = 2 x - 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x - 7)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

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

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

Expand $(2 x - 7) (2 x - 7)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

$f (2 x - 7) = 4 x^{2} + 2 x \cdot - 7 - 7 (2 x) - 7 \cdot - 7 - 5$

Multiply $- 7$ by $2$ .

$f (2 x - 7) = 4 x^{2} - 14 x - 7 (2 x) - 7 \cdot - 7 - 5$

Multiply $2$ by $- 7$ .

$f (2 x - 7) = 4 x^{2} - 14 x - 14 x - 7 \cdot - 7 - 5$

Multiply $- 7$ by $- 7$ .

$f (2 x - 7) = 4 x^{2} - 14 x - 14 x + 49 - 5$

Subtract $14 x$ from $- 14 x$ .

$f (2 x - 7) = 4 x^{2} - 28 x + 49 - 5$

Step 4

Subtract $5$ from $49$ .

$f (2 x - 7) = 4 x^{2} - 28 x + 44$