Answer:
Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=4x-3 \\ g(x)=\frac{1}{4}(x+3) \end{gathered}[/tex]a) We're to find f(g(x)).
To do this, we need to substitute x in f(x) with g(x) as shown below;
[tex]\begin{gathered} f(g(x))=4\lbrack\frac{1}{4}(x+3)\rbrack-3 \\ =(x+3)-3 \\ =x \end{gathered}[/tex]b) To find g(f(x)), we need to substitute x in g(x) with f(x);
[tex]\begin{gathered} g(f(x))=\frac{1}{4}\lbrack(4x-3)+3\rbrack \\ =\frac{1}{4}(4x) \\ =x \end{gathered}[/tex]c) Since f(g(x)) = g(f(x)) = x, therefore f and g are inverses of each other.
Yes, f and g are inverses of each other.
So to