The range of the function f ( x ) = 2 + x 2 − x , x ≠ 2 is Options: A . &nbsp R B . &nbsp R − { − 1 } C . &nbsp R − { 1 } D . &nbsp R − { − 2 }

Answer: Option B : B y = 2 + x 2 − x ⇒ 2 y − y x = 2 + x ⇒ x ( y + 1 ) = 2 y − 2 ⇒ x = 2 y − 2 y + 1 ⇒ f − 1 ( x ) = 2 x − 2 x + 1 ∴ Range of f = Domain of f − 1 = R − { − 1 }

The range of the function f(x)=2+x2−x,x≠2 is

Discussion Forum : Relations And Functions Ii

Question -

The range of the function $f (x) = \frac{2 + x}{2 - x}, x \neq 2$ is

Options:

A .

R

B .

R - {- 1}

C .

R - {1}

D .

R - {- 2}

Answer: Option B
:
B

y = \frac{2 + x}{2 - x} \Rightarrow 2 y - y x = 2 + x \Rightarrow x (y + 1) = 2 y - 2 \Rightarrow x = \frac{2 y - 2}{y + 1} \Rightarrow f^{- 1} (x) = \frac{2 x - 2}{x + 1}

∴

Range of

f =

Domain of

f^{- 1} = R - {- 1}

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