The function f(x)=(2x2+7/x3+3x2-x-3) is discontinuous for

Question

The function f(x)=(2x2+7/x3+3x2-x-3) is discontinuous for (A)  x=1 only (B)  x=1 and x=-1 only (C)  x=1, x=-1, x=-3 only (D)  x=1, x=-1, x=-3 and other values of x

Tardigrade Admin · Accepted Answer

Given, f(x)=(2x2+7/x3+3x2-x-3) =(2x2+7/(x2-1)(x+3)) At x=1, f(x)=∞ x=-1, f(x)=∞ x=-3, f(x)=∞ ∴ At x=1, x=-1 and x=-3 function is discontinuous

Q. The function $f (x) = \frac{2 x ^{2} + 7}{x ^{3} + 3 x ^{2} - x - 3}$ is discontinuous for

$x = 1$ only

$x = 1$ and $x = - 1$ only

$x = 1, x = - 1, x = - 3$ only

$x = 1, x = - 1, x = - 3$ and other values of x

Given, $f (x) = \frac{2 x ^{2} + 7}{x ^{3} + 3 x ^{2} - x - 3}$
$= \frac{2 x ^{2} + 7}{( x ^{2} - 1 ) ( x + 3 )}$
At $x = 1, f (x) = \infty$
$x = - 1, f (x) = \infty$
$x = - 3, f (x) = \infty$
$∴$ At $x = 1, x = - 1$
and $x = - 3$ function is discontinuous

Q. The function f(x)=x3+3x2−x−32x2+7​ is discontinuous for

x=1 only

x=1 and x=−1 only

x=1,x=−1,x=−3 only

x=1,x=−1,x=−3 and other values of x