Find g(f(x)) f(x)=2x-5 g(x)=x^2+1

$f (x) = 2 x - 5$ $g (x) = x^{2} + 1$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x - 5)$ by substituting in the value of $f$ into $g$ .

$g (2 x - 5) = {(2 x - 5)}^{2} + 1$

Step 3

Simplify each term.

Rewrite ${(2 x - 5)}^{2}$ as $(2 x - 5) (2 x - 5)$ .

$g (2 x - 5) = (2 x - 5) (2 x - 5) + 1$

Expand $(2 x - 5) (2 x - 5)$ using the FOIL Method.

Apply the distributive property.

$g (2 x - 5) = 2 x (2 x - 5) - 5 (2 x - 5) + 1$

Apply the distributive property.

$g (2 x - 5) = 2 x (2 x) + 2 x \cdot - 5 - 5 (2 x - 5) + 1$

Apply the distributive property.

$g (2 x - 5) = 2 x (2 x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 + 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$g (2 x - 5) = 2 \cdot (2 x \cdot x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 + 1$

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

Move $x$ .

$g (2 x - 5) = 2 \cdot (2 (x \cdot x)) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 + 1$

Multiply $x$ by $x$ .

$g (2 x - 5) = 2 \cdot (2 x^{2}) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 + 1$

Multiply $2$ by $2$ .

$g (2 x - 5) = 4 x^{2} + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 + 1$

Multiply $- 5$ by $2$ .

$g (2 x - 5) = 4 x^{2} - 10 x - 5 (2 x) - 5 \cdot - 5 + 1$

Multiply $2$ by $- 5$ .

$g (2 x - 5) = 4 x^{2} - 10 x - 10 x - 5 \cdot - 5 + 1$

Multiply $- 5$ by $- 5$ .

$g (2 x - 5) = 4 x^{2} - 10 x - 10 x + 25 + 1$

Subtract $10 x$ from $- 10 x$ .

$g (2 x - 5) = 4 x^{2} - 20 x + 25 + 1$

Step 4

Add $25$ and $1$ .

$g (2 x - 5) = 4 x^{2} - 20 x + 26$