Express the function in the form f ∘ g. (Use non-identity functions for f and g.)

Question

G(x) = cube root of x / ( 7 + x )

Answer 1

One way to express the function G(x) as a function in the form (f ο g), is to consider 2 functions so that when considered one after the other they are the composite function (f ο g).

We can observe that if we want to calculate G(x), given a value of x, first we need to calculate the value of the function x / ( 7 + x ), and then we need to calculate the cube root of the result. Therefore, this is a good example of a composite function if we call g(x) = x / ( 7 + x ) because it's the first function we compute, and then f(x) the cube root of x, because then we need to compute the cube root of the result of g(x).

f(x) = cube root of x

g(x) = x / ( 7 + x )

Therefore, we can see that the composite function G(x) can be expressed as

G(x) = (f ο g) (x) = f[g(x)] = cube root of [g(x)] = cube root of x / ( 7 + x )