we have the functions
[tex]f(x)=16x^2[/tex][tex]g(x)=\frac{1}{4}\sqrt[]{x}[/tex]
step 1
Find f(g(x))
[tex]f(g(x))=16(\frac{1}{4}\sqrt[]{x})^2[/tex]
simplify
[tex]f(g(x))=x[/tex]
therefore
Part 1
If x≥0 the value of f(g(x)) is x
step 2
Find g(f(x))
[tex]g(f(x))=\frac{1}{4}\sqrt[\square]{16x^2}[/tex]
simplify
[tex]g(f(x))=x[/tex]
therefore
Part 2
If x≥0 the value of g(f(x)) is the same as the first
step 3
Find the inverse of function f(x)
[tex]y=16x^2[/tex]
exchange the variables
[tex]x=16y^2[/tex]
isolate the variable y
[tex]\begin{gathered} y^2=\frac{x}{16} \\ y=\pm\frac{1}{4}\sqrt[\square]{x} \end{gathered}[/tex]
Part 3
the functions f(x) and g(x) are inverse functions
