Question

Need help with the composition of functions. I have attached a screenshot of the question.

Answer 1

h(h(x)) =
`x^(4)` + 6x² + 12

f(f(x)) = x

note that h ○ h = h(h(x))

To evaluate substitute h(x) into h(x)

h(h(x)) = h(x² + 3 ) = (x² + 3 )² + 3 =
`x^(4)` + 6x² + 9 + 3 =
`x^(4)` + 6x² + 12

Similarly for f ○ f

f(f(x)) = f(
`(9)/(2x)`)

= 9 / (2 ×
`(9)/(2x)` = 9 /
`(9)/(x)` =
`(9x)/(9)` = x