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Question

If h(x)=(fg)(x) and h1(x) is the inverse of h(x), then which of the following must be equal to x?

A
(h1fg)(x)
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B
(h1gf)(x)
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C
(f1g1h1)(x)
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D
(g1f1h1)(x)
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E
Not enough information
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Solution

The correct option is B (h1fg)(x)
f(f1(x))=x and f1(f(x))=x

Now
h(x)=f(g(x))

h1(h(x))=x

But L.H.S=h1(f(g(x)))

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