Find f(g(x)) f(x)=x^2+1 and g(x)=x-4

$f (x) = x^{2} + 1$ and $g (x) = x - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x - 4)$ by substituting in the value of $g$ into $f$ .

$f (x - 4) = {(x - 4)}^{2} + 1$

Step 3

Simplify each term.

Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$f (x - 4) = (x - 4) (x - 4) + 1$

Expand $(x - 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$f (x - 4) = x (x - 4) - 4 (x - 4) + 1$

Apply the distributive property.

$f (x - 4) = x \cdot x + x \cdot - 4 - 4 (x - 4) + 1$

Apply the distributive property.

$f (x - 4) = x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4 + 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

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

Multiply $- 4$ by $- 4$ .

$f (x - 4) = x^{2} - 4 x - 4 x + 16 + 1$

Subtract $4 x$ from $- 4 x$ .

$f (x - 4) = x^{2} - 8 x + 16 + 1$

Step 4

Add $16$ and $1$ .

$f (x - 4) = x^{2} - 8 x + 17$