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Question

Which of the following statements is (are) CORRECT?

A
The fundamental period of the function f(x)=cosec(x2)+sec(x3)+cot(x4)+tan(x5)+cos(x6)+sin(x7) is 420π.
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B
If f is a function such that f(s)=f(t), then s=t.
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C
A vertical line intersects the graph of a function at most once.
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D
If h(x)={x2,x0x,x>0, then h(h(x))=h(x) xR.
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Solution

The correct options are
A The fundamental period of the function f(x)=cosec(x2)+sec(x3)+cot(x4)+tan(x5)+cos(x6)+sin(x7) is 420π.
C A vertical line intersects the graph of a function at most once.
D If h(x)={x2,x0x,x>0, then h(h(x))=h(x) xR.
Period of f(x)= L.C.M. of ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪2π(12),2π(13),π(14),π(15),2π(16),2π(17)⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪

= L.C.M. of {4π,6π,4π,5π,12π,14π}
=420π

Clearly, f(s)=f(t) does not imply s=t
If f is one-one and f(s)=f(t), then s=t

Obviously, any vertical line intersects the graph of a function at most once.

We have h(x)={x2,x0x,x>0
But h(x)0 xR
So, h(h(x))={x2,x0x,x>0=h(x), xR

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