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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+4 log2 x)
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C
12(11+4 log2 x)
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D
not defined
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Solution

The correct option is B 12(1+1+4 log2 x)
Let y=2x(x1), where y1 as x1
Taking log2 on both sides, we get
log2 y=log2 2x(x1)
log2 y=x(x1)
x2xlog2 y=0
x=1±1+4log2y2
For y1,log2 y04 log2 y0 1+4log2 y1
1+4log2 y1
1+4log2 y1
11+4log2 y0
But x1
So, x=11+4log2 y is not possible.
Therefore, we take x=12(1+(1+4log2 y))
f1(y)=12(1+1+4log2 y)
f1(x)=12(1+1+4log2 y)

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