Question

For what values of m is f(x) = (m + 2)x³ – 3mx² + 9m x –1 is invertible?

Answer 1

Since the f is invertible, so f is one-one function. 

Given f(x) = (m + 2)x² – 3mx² + 9mx – 1 

⇒ f'(x) = 3(m + 2)x² – 6mx + 9m 

⇒ f'(x) = 3(m + 2)x² – 6mx + 9m > 0