Question

Consider f(x)=3/4 and g(x)=12x^2. Determine whether the domain of fg is the same as the domain of g or different.

Same or Not the same?

Answer 1

The domain of both of these functions is all real numbers. You can input anything into f(x), and regardless, you will get 3/4. g(x) is a polynomial (specifically a quadratic), which is defined for all real numbers.

The domain of a function
`(f*g)(x)` is the set where both f and g are defined. Mathematically, we use ∩ for intersection to show that
`D_(fg)=D_f` ∩
`D_g`. Here, it is just all real numbers for both g and fg.