Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let f(x) = 
. Determine the composite function g(x) = f (f(x)) & hence find the point of discontinuity of g , if any.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
g(x) = 2 + x ; 0 ≤ x ≤ 1,
= 2 − x ; 1 < x ≤ 2,
= 4 − x ; 2 < x ≤ 3,
g is discontinuous at x = 1 & x = 2
Sol. f(x) = 
y(x) = fof(x) = 
= 
g(1 – ) = g(1) = 3 ≠ g(1 + ) = 1 g(2 – ) = g(2) = 0 ≠ g(2 + ) = 2
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If f(x) = x + { − x} + [x], where [ . ] is the integral part & { . } is the fractional part functio…
If f(x) = and g(x) = tan x, then discuss the continuity of fog (x).
Let f(x) = . Determine the composite function g(x) = f (f(x)) & hence find the point of discontinu…
Find the point of discontinuity of y = f(u), where f(u) = and u =
Show that the function f(x) = – sin π x + 3 takes the value within the interval
[–2, 2].
If g(x) = (|x – 1| + |4x – 11|) [x 2 – 2x – 2], then find the number of point of discontinuity of g…