Algebra - domain and range of a function

GRE Quant Problem Solving
1

I don’t really understand why I got the answers wrong (I have re-watched prep swift videos on functions, even khan academy)

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why would for the first question, it is true? the range cannot be negative right given domain cannot be negative since it cannot be negative under the radical?

Similarly for the second question, why is it false? all real values are acceptable, right?

2

Write down what you think would be the domain and range for each for the two problems (with a short explanation).

3

For the first question: Domain = range = all values > 0

For the second question: Domain = range = all values

4

Can x^2 equal -1?