Question

f(x) = `{{:(0","                 x = 0 ), (x - 3","   x > 0):}` The function f(x) is ______

Options

• Increasing when x ≥ 0

• Strictly increasing when x > 0

• Strictly increasing at x = 0

• Not continuous at x = 0 and so it is not increasing when x > 0

Answer 1

f(x) = `{{:(0","                 x = 0 ), (x - 3","   x > 0):}` The function f(x) is Strictly increasing when x > 0.

Explanation:

f(x) = `{{:(0","                 x = 0 ), (x - 3","   x > 0):}` 

∴ f'(x) = `{{:(0","                 x = 0 ), (1","   x > 0):}` 

∴ lt is strictly increasing when x > 0.