Find f(g(x)) f(x)=x^2-25 , g(x)=2x+3

$f (x) = x^{2} - 25$ , $g (x) = 2 x + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x + 3)$ by substituting in the value of $g$ into $f$ .

$f (2 x + 3) = {(2 x + 3)}^{2} - 25$

Step 3

Simplify each term.

Rewrite ${(2 x + 3)}^{2}$ as $(2 x + 3) (2 x + 3)$ .

$f (2 x + 3) = (2 x + 3) (2 x + 3) - 25$

Expand $(2 x + 3) (2 x + 3)$ using the FOIL Method.

Apply the distributive property.

$f (2 x + 3) = 2 x (2 x + 3) + 3 (2 x + 3) - 25$

Apply the distributive property.

$f (2 x + 3) = 2 x (2 x) + 2 x \cdot 3 + 3 (2 x + 3) - 25$

Apply the distributive property.

$f (2 x + 3) = 2 x (2 x) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 - 25$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (2 x + 3) = 2 \cdot (2 x \cdot x) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 - 25$

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

Move $x$ .

$f (2 x + 3) = 2 \cdot (2 (x \cdot x)) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 - 25$

Multiply $x$ by $x$ .

$f (2 x + 3) = 2 \cdot (2 x^{2}) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 - 25$

Multiply $2$ by $2$ .

$f (2 x + 3) = 4 x^{2} + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3 - 25$

Multiply $3$ by $2$ .

$f (2 x + 3) = 4 x^{2} + 6 x + 3 (2 x) + 3 \cdot 3 - 25$

Multiply $2$ by $3$ .

$f (2 x + 3) = 4 x^{2} + 6 x + 6 x + 3 \cdot 3 - 25$

Multiply $3$ by $3$ .

$f (2 x + 3) = 4 x^{2} + 6 x + 6 x + 9 - 25$

Add $6 x$ and $6 x$ .

$f (2 x + 3) = 4 x^{2} + 12 x + 9 - 25$

Step 4

Subtract $25$ from $9$ .

$f (2 x + 3) = 4 x^{2} + 12 x - 16$