First slide

Functions (XII)

Question

If f and g arc one-one functions, then

Moderate

A

$f + g is one-one$
B

$f g is one-one$
C

$f o g is one-one$
D

$n o n e o f t h e s e$

Solution

$L e t f (x) = \sin x a n d g (x) = \cos x, x \in [0, \frac{π}{2}]$
$b o t h f a n d g a r e o n e o n e f u n c t i o n s b u t f + g = \sin x + \cos x i s n o t o n e o n e \sin c e (f + g) (0) = \sin 0 + \cos 0 = 1 a n d (f + g) (\frac{π}{2}) = 1$
$n o w (f g) (x) = \sin x \cdot \cos x, w h i c h i s n o t o n e o n e \sin c e (f g) (0) = 0 a n d (f g) (\frac{π}{2}) = 0$
hence options $(1), (2) a r e w r o n g . b u t f o g i s o n e o n e b y k n o w n t h e o r e m$

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