Find g(f(x)) f(x)=2^(x-1)+3 g(x)=5x-9

$f (x) = 2^{x - 1} + 3$ $g (x) = 5 x - 9$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2^{x - 1} + 3)$ by substituting in the value of $f$ into $g$ .

$g (2^{x - 1} + 3) = 5 (2^{x - 1} + 3) - 9$

Step 3

Simplify each term.

Apply the distributive property.

$g (2^{x - 1} + 3) = 5 \cdot 2^{x - 1} + 5 \cdot 3 - 9$

Multiply $5$ by $3$ .

$g (2^{x - 1} + 3) = 5 \cdot 2^{x - 1} + 15 - 9$

Step 4

Subtract $9$ from $15$ .

$g (2^{x - 1} + 3) = 5 \cdot 2^{x - 1} + 6$