combining functions

Question

f(x)=x3−4 and g(x)=x3

Step 1 of 2: Find the formula for (f∘g)(x) and simplify your answer.

Then find the domain for (f∘g)(x)

(f*g)(x)=???

Domain=???

Answer 1

Given f(x) = x³- 4 ; g(x) = x³

(f∗ g) (x) = f (g(x)) , meaning you are substituting g(x) for x in f(x) ;

=( x³)³ - 4

= x⁹ - 4

Domain : f(g(x)) is a polynomial; so the domain is all real numbers. You can write it using the interval notation as (–∞ . ∞ ).