Question

find composite functions
google classroom
microsoft teams
$g(x)=3-x^2$
$h(x)=4-3x$
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 $g(x)$

Replace $x$ in $g(x)$ with $h(x)=4-3x$:
$g(h(x)) = 3 - (4-3x)^2$

Step3: Expand the squared term

Expand $(4-3x)^2$ using $(a-b)^2=a^2-2ab+b^2$:
$(4-3x)^2 = 4^2 - 2\cdot4\cdot3x + (3x)^2 = 16 - 24x + 9x^2$

Step4: Simplify the expression

Substitute back and simplify:
$g(h(x)) = 3 - (16 - 24x + 9x^2) = 3 - 16 + 24x - 9x^2 = -9x^2 + 24x - 13$

Answer:

$\boldsymbol{-9x^2 + 24x - 13}$