Find f(g(x)) f(x)=4/5x-3 , g(x)=(5x+15)/4

$f (x) = \frac{4}{5} x - 3$ , $g (x) = \frac{5 x + 15}{4}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{5 x + 15}{4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{5 x + 15}{4}) = \frac{4}{5} \cdot (\frac{5 x + 15}{4}) - 3$

Step 3

Simplify each term.

Factor $5$ out of $5 x + 15$ .

Factor $5$ out of $5 x$ .

$f (\frac{5 x + 15}{4}) = \frac{4}{5} \cdot \frac{5 (x) + 15}{4} - 3$

Factor $5$ out of $15$ .

$f (\frac{5 x + 15}{4}) = \frac{4}{5} \cdot \frac{5 x + 5 \cdot 3}{4} - 3$

Factor $5$ out of $5 x + 5 \cdot 3$ .

$f (\frac{5 x + 15}{4}) = \frac{4}{5} \cdot \frac{5 (x + 3)}{4} - 3$

Cancel the common factor of $4$ .

Cancel the common factor.

$f (\frac{5 x + 15}{4}) = \frac{4}{5} \cdot \frac{5 (x + 3)}{4} - 3$

Rewrite the expression.

$f (\frac{5 x + 15}{4}) = \frac{1}{5} \cdot (5 (x + 3)) - 3$

Cancel the common factor of $5$ .

Cancel the common factor.

$f (\frac{5 x + 15}{4}) = \frac{1}{5} \cdot (5 (x + 3)) - 3$

Rewrite the expression.

$f (\frac{5 x + 15}{4}) = x + 3 - 3$

Step 4

Combine the opposite terms in $x + 3 - 3$ .

Subtract $3$ from $3$ .

$f (\frac{5 x + 15}{4}) = x + 0$

Add $x$ and $0$ .

$f (\frac{5 x + 15}{4}) = x$