The range of the function f(x) = (2+x/2-x) , x ≠ 2 is

Question

The range of the function f(x) = (2+x/2-x) , x ≠ 2 is (A)  R  (B) R- -1  (C) R- 1  (D) R -2

Tardigrade Admin · Accepted Answer

We have f(x)=y=(2+x/2-x) ⇒ 2 y-x y=2+x ⇒ 2 y-2=x+x y ⇒ 2 y-2=x(1+y) ⇒ x=(2 y-2/1+y) Since, x=(2 y-2/y+1) is defined if y+1 ≠ 0 i.e. y ≠-1 ∴ Range of f(x)=R- -1

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

$R$

$R - {- 1}$

$R - {1}$

$R {- 2}$

We have
$f (x) = y = \frac{2 + x}{2 - x}$
$\Rightarrow 2 y - x y = 2 + x$
$\Rightarrow 2 y - 2 = x + x y$
$\Rightarrow 2 y - 2 = x (1 + y)$
$\Rightarrow x = \frac{2 y - 2}{1 + y}$
Since, $x = \frac{2 y - 2}{y + 1}$ is defined if $y + 1 \neq = 0$ i.e. $y \neq = - 1$
$∴$ Range of $f (x) = R - {- 1}$

Q. The range of the function f(x)=2−x2+x​ , x=2 is

R

R−{−1}

R−{1}

R{−2}

We have f(x)=y=2−x2+x​ ⇒2y−xy=2+x ⇒2y−2=x+xy ⇒2y−2=x(1+y) ⇒x=1+y2y−2​ Since, x=y+12y−2​ is defined if y+1=0 i.e. y=−1 ∴ Range of f(x)=R−{−1}

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

$R$

$R - {- 1}$

$R - {1}$

$R {- 2}$