The distinct linear functions that map [-1, 1] onto [0, 2] are: - Vidyadip

MCQ

The distinct linear functions that map $[-1, 1]$ onto $[0, 2]$ are:

✓
$f(x) = x + 1, g(x) = -x + 1$
B
$f(x) = x - 1, g(x) = x + 1$
C
$f(x) = -x - 1, g(x) = x - 1$
D
None of these.

✓

Answer

Correct option: A.

$f(x) = x + 1, g(x) = -x + 1$

$f(x) = -x - 1, g(x) = x - 1$
Since $f$ is invertible, range of $f =$ co $-$ domain of $f = x$
So, we need to find the range of $f$ to find $X$.
For finding the range, let $f(x) = y$
$\Rightarrow 4x - x^2 = y$
$\Rightarrow x^2 - 4x = -y$
$\Rightarrow x^2 - 4x + 4 = 4 - y$
$\Rightarrow (x - 2)^2 = 4 - y$
$\Rightarrow {x}-2=\pm4-{y}$
$\Rightarrow {x}=2\pm4-{y}$
This is defined only when $4-{y}\geq0$
$\Rightarrow {y}\leq4,$
$X =$ Range of $f =(-\infty,4]$

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