Continuity and DifferentiabilityMedium
Question
Indicate all correct alternatives if, f(x) = 
- 1, then on the interval [0, π]
- 1, then on the interval [0, π]Options
A.tan (f (x)) & 
are both continuous
are both continuousB.tan (f (x)) & are both discontinuous
are both discontinuousC.tan (f (x)) & f-1 (x) are both continuous
D.tan (f (x)) is continuous but 
is not
is notSolution
(i) tan f(x) = tan 
x ∈ [0, π]
0 ≤ x ≤ π ⇒ -1 ≤
- 1 ≤ 
- 1
By graph we say tan(f(x)) is continuous in [0, π]
(ii)
is not defined at x = 2 ∈ [0, π]
(iii) y =
f-1(x) = 2x + 2 is continuous in R.
x ∈ [0, π]0 ≤ x ≤ π ⇒ -1 ≤
- 1 ≤ - 1By graph we say tan(f(x)) is continuous in [0, π]
(ii)
is not defined at x = 2 ∈ [0, π](iii) y =
f-1(x) = 2x + 2 is continuous in R.
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