Find h(g(x)) g(x)=(x+8)/5 and h(x)=5(x-8)

$g (x) = \frac{x + 8}{5}$ and $h (x) = 5 (x - 8)$

Set up the composite result function.

$h (g (x))$

Evaluate $h (\frac{x + 8}{5})$ by substituting in the value of $g$ into $h$ .

$h (\frac{x + 8}{5}) = 5 ((\frac{x + 8}{5}) - 8)$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$h (\frac{x + 8}{5}) = 5 (\frac{x + 8}{5} - 8 \cdot \frac{5}{5})$

Simplify terms.

Combine $- 8$ and $\frac{5}{5}$ .

$h (\frac{x + 8}{5}) = 5 (\frac{x + 8}{5} + \frac{- 8 \cdot 5}{5})$

Combine the numerators over the common denominator.

$h (\frac{x + 8}{5}) = 5 (\frac{x + 8 - 8 \cdot 5}{5})$

Simplify the numerator.

Multiply $- 8$ by $5$ .

$h (\frac{x + 8}{5}) = 5 (\frac{x + 8 - 40}{5})$

Subtract $40$ from $8$ .

$h (\frac{x + 8}{5}) = 5 (\frac{x - 32}{5})$

Cancel the common factor of $5$ .

Cancel the common factor.

$h (\frac{x + 8}{5}) = 5 (\frac{x - 32}{5})$

Rewrite the expression.

$h (\frac{x + 8}{5}) = x - 32$