Question

If f(x) = x-1/3 and g(x) = 3x+1 , what is the domain of (f*g)(x) ?

Answer 1

-∞ < x < ∞

Set of all integers

Explanation:

Given in the question two functions

f(x) =
`x^{(1)/(3) }` = ∛x

g(x) = 3x + 1

(f*g)(x)

f(g(x))

∛(3x+1)

Domain of (f*g)(x)

In function ∛(3x+1) , variable x can be any integer.

so, the domain is set of all integers

-∞ < x < ∞