Question

Let f(x) = $\frac {x^4-5x^2+4} {|(x-1) (x-2)|}$ , x $\neq$ 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)

R - {1, 2}

Answer 2

$f(x) = \frac {(x^2 - 1)(x^2-4)} {[(x-1) (x-2)]}$ Since $\lim_{x\to1} \frac{x-1}{\left|x-1\right|}$ does not exist. $\lim_{x\to2} \frac{x-1}{\left|x-1\right|}$ does not exist. $\therefore$ $\lim_{x\to1} f(x)$ and $\lim_{x\to2} f(x)$ 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}.