Find f(g(x)) f(x)=4x-3 and g(x)=1/4x+3

$f (x) = 4 x - 3$ and $g (x) = \frac{1}{4} x + 3$

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{1}{4} x + 3)$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{4} x + 3) = 4 (\frac{1}{4} x + 3) - 3$

Simplify each term.

Combine $\frac{1}{4}$ and $x$ .

$f (\frac{1}{4} x + 3) = 4 (\frac{x}{4} + 3) - 3$

Apply the distributive property.

$f (\frac{1}{4} x + 3) = 4 (\frac{x}{4}) + 4 \cdot 3 - 3$

Cancel the common factor of $4$ .

Cancel the common factor.

$f (\frac{1}{4} x + 3) = 4 (\frac{x}{4}) + 4 \cdot 3 - 3$

Rewrite the expression.

$f (\frac{1}{4} x + 3) = x + 4 \cdot 3 - 3$

Multiply $4$ by $3$ .

$f (\frac{1}{4} x + 3) = x + 12 - 3$

Subtract $3$ from $12$ .

$f (\frac{1}{4} x + 3) = x + 9$