Find f(g(x)) f(x)=2x-3 and g(x)=1/2x+3

$f (x) = 2 x - 3$ and $g (x) = \frac{1}{2} x + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\frac{1}{2} x + 3) = 2 (\frac{1}{2} x + 3) - 3$

Step 3

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

$f (\frac{1}{2} x + 3) = 2 (\frac{x}{2} + 3) - 3$

Apply the distributive property.

$f (\frac{1}{2} x + 3) = 2 (\frac{x}{2}) + 2 \cdot 3 - 3$

Cancel the common factor of $2$ .

Cancel the common factor.

$f (\frac{1}{2} x + 3) = 2 (\frac{x}{2}) + 2 \cdot 3 - 3$

Rewrite the expression.

$f (\frac{1}{2} x + 3) = x + 2 \cdot 3 - 3$

Multiply $2$ by $3$ .

$f (\frac{1}{2} x + 3) = x + 6 - 3$

Step 4

Subtract $3$ from $6$ .

$f (\frac{1}{2} x + 3) = x + 3$