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Question

If the function f:[1,)[1,) is defined by f(x)=2x(x1), then f1(x) is

A
(12)x(x1)
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B
(12)(1+1+4log2x)
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C
(12)(11+4log2x)
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D
Not defined
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Solution

The correct option is B (12)(1+1+4log2x)
f(x)=2x(x+1), i.e., y=2x(x+1),

log2y=x(x1)=x2x

x2xlog2y=0

x=1±1+4log2y2

Since x[1,) -ve sign is ruled out.

x=12(1+1+4log2y)

f1(x)=12(1+1+4log2y)

f1(x)=12(1+1+4log2x)

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