Question

Question in image, it asks to show your work

Answer 1

• f(g(x)) =
`\sqrt{x^(2) + 1}` + 8

• g(f(x)) = 16
`√(x)` + x + 65

Explanation:

• f(g(x)) = f(x² + 1)

=
`\sqrt{x^(2) + 1}` + 8

• g(f(x)) = g(
`√(x + 8)` )

=
`(√(x ) + 8)^(2)` + 1

= x + 16
`√(x)` + 64 + 1

= 16
`√(x)` + x + 65