Question

Let f(x) = $\frac{x^4-5x^2+4}{|(x-1)(x-2)|}$ , x $\ne$ 1,2 = 6 ,x=1,12, x = 2, Then f (x) is continuous on the set

• A. R
• B. R-{1}
• C. R-{2}
• D. R - {1, 2}

Answer 1

Answer: (D)

$f(x)=\frac{(x^2-1)(x^2-4)}{[(x-1)(x-2)]}$
Since ${\lim }_{x\to 1}\frac{x-1}{|x-1|}$ does not exist.
${\lim }_{x\to 2}\frac{x-1}{|x-1|}$ does not exist.
$\therefore$ ${\lim }_{x\to 1}f(x)$ and ${\lim }_{x\to 2}f(x)$ do not exist.
$\therefore$ $f(x)$ is not continuous at $x$ = 1, 2 At all other points $f(x)$ is continuous
$\therefore$ $f(x)$ is continuous on R - {1, 2}.