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Perform the indicated operation and state the domain. Let f(x) = 3x^1/3 and g(x) = 2x^1/2 Express as (f+g)(x)

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MrRoyalidn

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]

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