Let f(x)=2×5−8×2+11×4+4×3+8×2+8x+4. Then A={x:f is continuous at x} is equal to

Let $f (x) = \frac{2 x^{5} - 8 x^{2} + 11}{x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4}$ . Then
$A = {x : f$ is continuous at $x}$ is equal to

A
$R$
B
$R ~ {0}$
C
$R ~ {- 1}$
D
$R ~ {- 1 - 2}$

Solution:

$x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4 = {(x^{2} + 2 x + 2)}^{2}$

and $x^{2} + x + 2 = (x + 1)^{2} + 1$ so $x^{4} + 4 x^{3} + 8 x^{2}$

$+ 8 x + 4 \neq 0$ for any $x .$ Hence $f$ is a continuous function.

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