Question

find (f∘g)(-3) and (g∘f)(-3).
f(x) = -4x - 1; g(x) = x² - 4
(f∘g)(-3) =
(g∘f)(-3) =

Explanation:

Step1: Compute $g(-3)$

$g(-3) = (-3)^2 - 4 = 9 - 4 = 5$

Step2: Compute $(f\circ g)(-3)=f(g(-3))$

$f(5) = -4(5) - 1 = -20 - 1 = -21$

Step3: Compute $f(-3)$

$f(-3) = -4(-3) - 1 = 12 - 1 = 11$

Step4: Compute $(g\circ f)(-3)=g(f(-3))$

$g(11) = (11)^2 - 4 = 121 - 4 = 117$

Answer:

$(f\circ g)(-3) = -21$
$(g\circ f)(-3) = 117$