Question

If ​f(x) = class="latex-formula"> 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

Answer:

Step-by-step explanation:

Given are two functions f and g defined as

$f(x) =\sqrt{x} \\g(x) = x^3+8$

we have to find the composition of functions in all orders

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

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

$c) (gof)(x) = g(\sqrt{x}) = (\sqrt{x})^3+3 = x^{\frac{3}{2} } +8\\\\d)(fog)(x)=f{g(x)}=f(x^3+8)$