Functions Ques 8
- There are exactly two distinct linear functions, …, and… which map $\{-1,1\}$ onto $\{0,2\}$.
$(1989,2 \mathrm{M})$
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Answer:
Correct Answer: 8.$( y = x + 1$ and $ y =- x + 1)$
Solution: Let $y=a x+b$ and $y=c x+d$ be two linear functions.
When $\quad x=-1, y=0$ and $x=1, y=2$, then
$ 0=-a+b \text { and } a+b=2 \Rightarrow a=b=1 $
$\therefore \quad y=x+1$
Again, when $x=-1, y=2$ and $x=1, y=0$, then
$ \begin{aligned} & -c+d=2 \text { and } c+d=0 \\ & \Rightarrow \quad d=1 \text { and } c=-1 \\ & \therefore \quad y=-x+1 \\ \end{aligned} $
Hence, two linear functions are $y=x+1$ and $y=-x+1$
BETA
