Find the Domain f(x)=1/(1+ square root of x)

Problem

ƒ(x)=1/(1+√(,x))

Solution

1. Identify the restriction for the square root function. For √(,x) to be defined in the set of real numbers, the radicand must be non-negative.

x≥0

2. Identify the restriction for the fraction. The denominator of a fraction cannot be equal to zero.

1+√(,x)≠0

3. Solve the inequality for the denominator. Since √(,x) is always greater than or equal to 0 for all x≥0 the expression 1+√(,x) is always greater than or equal to 1

1+√(,x)≥1

4. Conclude that the denominator 1+√(,x) is never zero for any x in the domain of the square root. Therefore, the only restriction on the function is x≥0

Final Answer

Domain:[0,∞)

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