The compositions are:
- f(g(x)) = x
- g(f(x)) = x
- We conclude that the functions are inverse functions.
How to find the compositions of the functions?
Here we have:
[tex]f(x) = 16*x^2\\\\g(x) = \frac{1}{4}\sqrt{x}[/tex]
The compositions are:
[tex]f(g(x)) = 16*(g(x))^2 = 16*(\frac{1}{4} \sqrt{x} )^2 = 16*\frac{1}{16}*x = x\\\\g(f(x)) = \frac{1}{4}*\sqrt{f(x)} = \frac{1}{4} \sqrt{16x^2} = x[/tex]
Then we can conclude that for x ≥ 0 (because we can evaluate the square root in x < 0) that f(x) and g(x) are inverse functions.
If you want to learn more about inverse functions:
https://brainly.com/question/14391067
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