Question

find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x) = 4x and g(x) = 4x f(g(x)) =

Explanation:

Step1: Substitute g(x) into f(x)

$f(g(x)) = f(4x) = 4(4x)$

Step2: Simplify the expression

$f(g(x)) = 16x$

Step3: Substitute f(x) into g(x)

$g(f(x)) = g(4x) = 4(4x)$

Step4: Simplify the expression

$g(f(x)) = 16x$

Step5: Check inverse condition

For inverses, $f(g(x))=x$ and $g(f(x))=x$ must hold.

Answer:

$f(g(x)) = 16x$
$g(f(x)) = 16x$
The functions $f$ and $g$ are not inverses of each other, since $f(g(x))
eq x$ and $g(f(x))
eq x$.