Question

y = $f(x) = 2^{x(x - 1)}$ where t =$f^{- 1}(x)$, then the number of points of discontinuities of y = f(x), x ∈ R is-

• A. 1
• B. 2
• C. 3
• D. Infinite

Answer 1

Answer: (C)

3

Answer 2

t = $\frac { 1 } { x - 1 }$ is discontinuous at x = 1

y = is discontinuous at t = – 2 and t = 1

t = – 2, $\frac { 1 } { x - 1 }$ = – 2 ⇒ x = 1/2

t = 1, $\frac { 1 } { x - 1 }$ = 1 ⇒ x = 2

y = f(x) is discontinuous at three points 1, $\frac { 1 } { 2 }$, 2.