find f + g, f - g, fg, and $\frac{f}{g}$. determine the domain for each function.\nf(x) = $sqrt{x}$; g(x) =…

find f + g, f - g, fg, and $\frac{f}{g}$. determine the domain for each function.\nf(x) = $sqrt{x}$; g(x) = x - 18\n(f + g)(x) = $sqrt{x}$ + x - 18 (simplify your answer.)\nwhat is the domain of f + g?\na. the domain of f + g is { }. (use a comma to separate answers as needed.)\nb. the domain of f + g is 0,$infty$). (type your answer in interval notation.)\nc. the domain of f + g is $varnothing$.\n(f - g)(x) = (simplify your answer.)

find f + g, f - g, fg, and $\frac{f}{g}$. determine the domain for each function.\nf(x) = $sqrt{x}$; g(x) = x - 18\n(f + g)(x) = $sqrt{x}$ + x - 18 (simplify your answer.)\nwhat is the domain of f + g?\na. the domain of f + g is { }. (use a comma to separate answers as needed.)\nb. the domain of f + g is 0,$infty$). (type your answer in interval notation.)\nc. the domain of f + g is $varnothing$.\n(f - g)(x) = (simplify your answer.)

Answer

Explanation:

Step1: Find (f - g)(x)

Subtract g(x) from f(x). So, (f - g)(x)=f(x)-g(x)=\sqrt{x}-(x - 18)=\sqrt{x}-x + 18

Step2: Determine the domain of (f - g)(x)

The function f(x)=\sqrt{x} is defined when x\geq0. The function g(x)=x - 18 is defined for all real - numbers. The domain of (f - g)(x) is determined by the domain of f(x) since the square - root function has a more restrictive domain. So the domain of (f - g)(x) is [0,\infty).

Answer:

(f - g)(x)=\sqrt{x}-x + 18 The domain of f - g is [0,\infty)