Consider the function f(x)= \ (x+5)/(x-2) if x ≠ 2 1 if x=2 \ Then f(f(x)) is discontinuous

Correct answer: (B) at exactly two values of x. f(x)= \ (x+5)/(x-2), x ≠ 2 1, x=2 . f(x) is discontinuous at x=2 f(x)=2 ⇒ (x+5)/(x-2)=2 ⇒ x+5=2 x-4 ⇒ x=9

Q42 / 90 · KVPY 2014 (SB/SX) · Mathematics

Consider the function $$ f(x)=\left\{\begin{array}{ll} \frac{x+5}{x-2} & \text { if } x \neq 2 \\ 1 & \text { if } x=2 \end{array}\right\} $$ Then $\mathrm{f}(\mathrm{f}(\mathrm{x}))$ is discontinuous

A
at all real numbers
Correct answer
B
at exactly two values of $x$
C
at exactly one value of $x$
D
at exactly three values of $x$

Solution

$f(x)=\left\{\begin{array}{ll}\frac{x+5}{x-2}, & x \neq 2 \\ 1, & x=2\end{array}\right.$ $f(x)$ is discontinuous at $x=2$ $f(x)=2$ $$ \Rightarrow \frac{x+5}{x-2}=2 $$ $$ \begin{array}{l} \Rightarrow x+5=2 x-4 \\ \Rightarrow x=9 \end{array} $$

Hence, the correct answer is option: 'B'.

Consider the function $$ f(x)=\left\{\begin{array}{ll} \frac{x+5}{x-2} & \text { if } x \neq 2 \\ 1 & \text { if } x=2 \end{array}\right\} $$ Then $\mathrm{f}(\mathrm{f}(\mathrm{x}))$ is discontinuous

Solution

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