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If f(x) = 2x + |x|, g(x) = 1/3 (2x - |x|) and h(x) = f(g(x)), then domain of sin-1(h(h(h(h........h.h(x)........)))) { in brackets.. h(x) is n times} is:
a. [-1, 1]
b. [-1, -1/2] U [1/2. 1]
c. [-1, -1/2]
d. [1/2, 1]
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2 Answers
11let us assume that x>0
so
f(x)=3x and g(x)=x/3
f(g(x))=x=h(x)
sin-1(x.x.x.x.x.....x)(n times)
we get
sin-1xn
and we know that the domain of sin-1x is [0 ,1](x>0)
if x<0
we will get f(g(x))=x
so again
sin-1xn
and we know that the domain of sin-1x is [-1 ,0](x<0)
so A is correct