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Find the domain of the real function f(x) defined by f(x) = {{

Question

Find the domain of the real function f(x) defined by $f (x) = \frac{1 - ∣ x ∣}{2 - ∣ x ∣}$

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Find the domain of the real function f(x) defined by

f (x) = \frac{1 - ∣ x ∣}{2 - ∣ x ∣}

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Text solutionVerified

f (x) = \frac{1 - ∣ x ∣}{2 - ∣ x ∣}

For definition of

f (x), \frac{1 - ∣ x ∣}{2 - ∣ x ∣} \geq 0

ase (1) when

1 - ∣ x ∣ \geq 0

and

2 - ∣ x ∣ > 0

\Rightarrow - 1 \leq x \leq 1

and

- 2 < x < 2

\Rightarrow x \in [- 1, 1]

Case (2) when

1 - ∣ x ∣ \leq 0

and

2 - ∣ x ∣ < 0

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

and

x \in (- \infty, - 2) \cup (2, \infty)

\Rightarrow x \in (- \infty, 2) \cup ((2, \infty)

\Rightarrow

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

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Question Text	Find the domain of the real function *f(x)* defined by $f (x) = \frac{1 - ∣ x ∣}{2 - ∣ x ∣}$
Answer Type	Text solution:1
Upvotes	150