Continuity and DifferentiabilityHard

Question

Indicate all correct alternatives if, f(x) = - 1, then on the interval [0, π]

Options

A.tan (f (x)) & are both continuous
B.tan (f (x)) & are both discontinuous
C.tan (f (x)) & f-1 (x) are both continuous
D.tan (f (x)) is continuous but is not

Solution

(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.

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