Question

if $f(x) = x^2 - 2$ and $g(x) = x + 4$, find $(f \circ g)(3)$ and $(g \circ f)(-3).$
a) $(f \circ g)(3)$
$(f \circ g)(3) = $
b) $(g \circ f)(-3)$

Explanation:

Step1: Compute $g(3)$ first

$g(3) = 3 + 4 = 7$

Step2: Substitute into $f(x)$ for $(f\circ g)(3)$

$(f\circ g)(3) = f(g(3)) = f(7) = 7^2 - 2 = 49 - 2 = 47$

Step3: Compute $f(-3)$ first

$f(-3) = (-3)^2 - 2 = 9 - 2 = 7$

Step4: Substitute into $g(x)$ for $(g\circ f)(-3)$

$(g\circ f)(-3) = g(f(-3)) = g(7) = 7 + 4 = 11$

Answer:

a) $(f \circ g)(3) = 47$
b) $(g \circ f)(-3) = 11$