Answer 1

f(x) = x² + 2x - 5 

∴ f'(x) = 2x + 2

f(x) is an increasing function, if f'(x) > 0

∴ 2x + 2 > 0

∴ 2x > -2

∴ x > - 1

Thus, f(x) is an increasing function for x > -1, i.e., (-1, ∞)