First slide

Functions (XII)

Question

The function $f : (- \infty, - 1] \to (0, e^{5}]$ defined by $f (x) = e^{x^{3} - 3 x + 2}$ is

Difficult

A

many-one and onto
B

many-one and into
C

one-one and onto
D

one-one and into

Solution

$\begin{array}{l} f (x) = e^{x^{3} - 3 x + 2} \\ Let g (x) = x^{3} - 3 x + 2; \\ g' (x) = 3 x^{2} - 3 = (x^{2} - 1) \\ \geq 0 for x \in (- \infty, - 1] \end{array}$
Therefore, $f (x)$ is increasing function. Hence $f (x)$ is one-one.
Now, the rang e of $f (x)$ is $(0, e^{4}]$ .
But co-domain is $(0, e^{5}]$
Hence, $f (x)$ is an into function.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App