Compare the given graphs of f(x) = 2√x and g(x) = 2∛x and determine which of the following is true.

Question

• When x > 1, the function g(x) = 2∛x is greater than f(x) = 2√x.
• The graphs have different domains.
• Both graphs go through (-1, -1), (0, 0), and (1, 1).
• They are both decreasing on their domains.

Answer 1

The first statement is not true. When x > 1, g(x) = 2∛x will be less than f(x) = 2√x.

The second statement is also not true. The domain of both functions is x ≥ 0.

The third statement is true. If we substitute x = -1, 0, and 1 into both functions, we get the same y-values: (-1, -1), (0, 0), and (1, 1).

The fourth statement is not true. The function f(x) = 2√x is increasing on its domain (x ≥ 0), while the function g(x) = 2∛x is also increasing on its domain (x ≥ 0).

So, the only statement that is true is that both graphs go through (-1, -1), (0, 0), and (1, 1).