First slide

Functions (XII)

Question

$Let f : R \to R, be defined as f (x) = e^{x^{2}} + \cos x, then f is$

Moderate

A

one-one and onto
B

one-one and into
C

many-one and onto
D

many-one and into

Solution

$f (x) = e^{x^{2}} + \cos x i s e v e n f u n c t i o n, s o i t i s n o t o n e - o n e (i . e m a n y o n e)$
$a l s o f (x) i s n o t o n t o \sin c e e^{x^{2}} \geq 1 \Rightarrow e^{x^{2}} + \cos x > 0$
$R a n g e o f f (x) i s (0, \infty) w h i c h i s n o t e q u a l t o c o d o m a i n R h e n c e f i s i n t o$

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