Let f (x) and g(x) be defined as
f(x) = 
and g(x) = 
.
Examine the continuity of gof.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. f(x) = 
and
g(x) = 
For x < 0, we have
gof (x) = g(f(x)) = g (x 3 + 1) = 
= x
For 0 ≤ x < 
, we have
gof (x) = g (f(x)) = g(x 2 –1) = 
= 
For x ≥ 2 
, we have
gof (x) = g(f(x)) = g(x 2 –1) = 
= |x| = x
Thus, we have
h(x) = gof (x) = 
Possible points of discontinuity are x = 0,
at x = 0;
h(x) = 
x = 0
h(x) = 
= (–2) 1/3 and h(0) = (–2) 1/3
thus 
h(x) ≠ 
h(x)
∴ h(x) is not continuous at x = 0 at x = 
(h(x)) = 
= 0
h(x) = 
+ x = 
∴ h(x) is not continuous at x = 
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