Question

find composite functions
google classroom microsoft teams
$g(x) = \frac{8x - 1}{x + 4}$
$h(x) = 3x + 10$
write $(g \circ h)(x)$ as an expression in terms of $x$.
$(g \circ h)(x) = $

Explanation:

Step1: Define composite function

$(g \circ h)(x) = g(h(x))$

Step2: Substitute $h(x)$ into $g$

Substitute $h(x)=3x+10$ for $x$ in $g(x)$:
$g(h(x)) = \frac{8(3x+10) - 1}{(3x+10) + 4}$

Step3: Expand numerator

Calculate the expanded numerator:
$8(3x+10)-1 = 24x + 80 - 1 = 24x + 79$

Step4: Simplify denominator

Calculate the simplified denominator:
$(3x+10)+4 = 3x + 14$

Step5: Combine results

Combine the simplified numerator and denominator.

Answer:

$\frac{24x + 79}{3x + 14}$