First slide

Functions (XII)

Question

$Let A = [a, \infty) denotes domain, then f : [a, \infty) \to B, f (x) = 2 x^{3} - 3 x^{2} + 6 will have an inverse for$ $the smallest real value of a, if :$

Moderate

A

$a = 1, B = [5, \infty)$
B

$a = 2, B = [10, \infty)$
C

$a = 0, B = [6, \infty)$
D

$a = - 1, B = [1, \infty)$

Solution

$\begin{array}{l} f (x) = 2 x^{3} - 3 x^{2} + 6 \\ f^{'} (x) = 6 x^{2} - 6 x \geq 0 \Rightarrow x \in [1, \infty) \\ and f (x) \in [5, \infty) \end{array}$

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