Question

Given f(x)=1/x-2 and g(x)=square root of x+2, what is the domain of f (g(x))?.A. ℝB. [–2, ∞)C. [–2, 2) ∪ (2, ∞)D. (–∞, 2) ∪ (2, ∞)

Answer 1

we have the functions

`\begin{gathered} f(x)=(1)/(x-2) \\ \\ g(x)=√(x+2) \end{gathered}`

Find out f(g(x))

`f\mleft(g\mleft(x\mright)\mright)=(1)/(√(x+2)-2)`

Remember that

The radicand must be greater than or equal to zero and the denominator cannot be equal to zero

so

step 1

Solve the inequality

the solution to the first inequality is the interval [-2, infinite)

step 2

Solve the equation

The domain is the interval

[–2, 2) ∪ (2, ∞)

The answer is the option C