The domain of defined of the function f(x)={1-|x|/2-|x|} is ____

Correct Answer is : [−1,1]∪(−∞,−2)∪(2,∞)[-1,1] (-∞,-2) (2,∞)[−1,1]∪(−∞,−2)∪(2,∞)

Correct Answer is : [−1,1]∪(−∞,−2)∪(2,∞)[-1,1] (-∞,-2) (2,∞)[−1,1]∪(−∞,−2)∪(2,∞)

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AP EAPCET 24-Aug-2021 Shift 1 Paper

Section: Mathematics

Question : 2 of 160

Marks: +1, -0

f(x)=\sqrt{\frac{1-|x|}{2-|x|}}

is ____

Solution:

f(x)=\sqrt{\frac{1-|x|}{2-|x|}}

For domain

\frac{1-|x|}{2-|x|} \geq 0

...(i)

and

2-|x| \neq 0

|x| \neq 2

x=\pm 2

Case I When,

x \geq 0

So, Eq. (i) becomes

\frac{1-x}{2-x} \geq 0\;\;\;\;

\{ \because |x| = \begin{bmatrix} x & x \geq 0 \\ -x & x < 0 \end{bmatrix} \}

Now, critical points are

x=1,2

Using wavy curve method

But

x \geq 0

Solution is

x \in [0,1] \cup (2,\infty)

Case II When,

x<0

So, Eq. (i) becomes

\frac{1+x}{2+x} \geq 0

Critical points are

x=-1,-2

Using wavy curve method

But

x<0

Solution is

x \in (-\infty,-2) \cup [-1,0)

∴ Required solution is union of case I and case Il.

∴ Required solution is

x \in (-\infty,-2) \cup [-1,1] \cup (2,\infty)

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