If ​f(x) = √(x) and ​g(x) = x cubed plus 8​, simplify the expressions (f circle g )(2 )​, (f circle f )(25 )​, (g circle f )(x )​, and (f circle g )(x ).

Question

If ​f(x) =
`√(x)` and ​g(x) = x cubed plus 8​, simplify the expressions (f circle g )(2 )​, (f circle f )(25 )​, (g circle f )(x )​, and (f circle g )(x ).

Answer 1

Explanation:

Given are two functions f and g defined as

`f(x) =√(x) \\g(x) = x^3+8`

we have to find the composition of functions in all orders

1)
`a)(fog)(x)=f{g(x)}=f(x^3+8) =√(x^3+8) \\\\(fog)(2) = =4,-4`

`b) (fof)(x) = f{f(x)}=f(√(x) {=\sqrt[4]{x} \\\\When x=25, ans= √(5)`

`c) (gof)(x) = g(√(x)) = (√(x))^3+3 = x^{(3)/(2) } +8\\\\d)(fog)(x)=f{g(x)}=f(x^3+8)`