Answer:
[tex](f + g)(x) = 3x^{\frac{1}{3}}+2x^{\frac{1}{2}}[/tex]
[tex]x \ge 0[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 3x^{\frac{1}{3}}[/tex]
[tex]g(x) = 2x^{\frac{1}{2}}[/tex]
Solving (a): (f + g)(x)
In functions:
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 3x^{\frac{1}{3}}+2x^{\frac{1}{2}}[/tex]
Solving (b): The domain of f(x)
For (f + g)(x) to be defines, the value of x must be greater than or equal to 0.
Hence, the domain is:
[tex]x \ge 0[/tex]
