Number of linear functions be defined f:[−1, 1]→[0,2] is a)1 b)2 c)3 d)4


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Question Number 184739 by SLVR last updated on 11/Jan/23

$N u m b e r o f l i n e a r f u n c t i o n s$ $b e d e f i n e d f : [- 1, 1] \to [0, 2] i s$ $a) 1 b) 2 c) 3 d) 4$
Commented by SLVR last updated on 11/Jan/23

$k i n d l y h e l p m e . . a n s w e r s a y s$ $2 o n l y . . h o w$
	Answered by mr W last updated on 11/Jan/23

	$i n d o m a i n [- 1, 1] t h e l i n e a r f u n c t i o n$ $f (x) = a x + b h a s t h e r a n g e$ $[- a + b, a + b] i f a > 0 (c a s e 1)$ $o r$ $[a + b, - a + b] i f a < 0 (c a s e 2)$ $s i n c e t h e r a n g e s h o u l d b e [0, 2],$ $c a s e 1 :$ $- a + b = 0$ $a + b = 2$ $\Rightarrow a = 1, b = 1 \Rightarrow f (x) = x + 1$ $c a s e 2 :$ $a + b = 0$ $- a + b = 2$ $\Rightarrow a = - 1, b = 1 \Rightarrow f (x) = - x + 1$ $i . e . t h e r e a r e 2 f u n c t i o n s s a t i s f y i n g$ $t h e g i v e n c o n d i t i o n s :$ $f (x) = x + 1 o r f (x) = - x + 1$
	Commented by SLVR last updated on 11/Jan/23

	$S o g r e a t o f y o u s i r . . .$ $s o k i n d o f y o u s i r . . T h a n k s a g a i n$
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