If x ∈ R then range of f(x)=(x2+2 x-3/2 x2+3 x-9) is:

Question

If x ∈ R then range of f(x)=(x2+2 x-3/2 x2+3 x-9) is: (A) (-∞, ∞) (B) R - (1/2)  (C) R - (4/9), (1/2)  (D) R - (3/2)

Tardigrade Admin · Accepted Answer

f(x)=((x+3)(x-1)/(2 x-3)(x+3)) x ≠-3, (3/2) f(x)=y-=(x-1/2 x-3) ; 2 x y-3 y=x-1 x=(3 y-1/2 y-1) ∴ y ≠ (1/2) But since x ≠-3 hence y=(4/9). ∴ y ∈ R- (4/9), (1/2)

Q. If $x \in R$ then range of $f (x) = \frac{x ^{2} + 2 x - 3}{2 x ^{2} + 3 x - 9}$ is:

$(- \infty, \infty)$

$R - {\frac{1}{2}}$

$R - {\frac{4}{9}, \frac{1}{2}}$

$R - {\frac{3}{2}}$

$f (x) = \frac{( x + 3 ) ( x - 1 )}{( 2 x - 3 ) ( x + 3 )}$
$x \neq = - 3, \frac{3}{2}$
$f (x) = y - = \frac{x - 1}{2 x - 3}; 2 x y - 3 y = x - 1$
$x = \frac{3 y - 1}{2 y - 1}$
$∴ y \neq = \frac{1}{2}$
But since $x \neq = - 3$ hence $y = \frac{4}{9}$ .
$∴ y \in R - {\frac{4}{9}, \frac{1}{2}}$

Q. If x∈R then range of f(x)=2x2+3x−9x2+2x−3​ is:

(−∞,∞)

R−{21​}

R−{94​,21​}

R−{23​}