BPSC 46th Exam Prelims 2004 Solved Paper

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Question : 135 of 150

Marks: +1, -0

If

f (x) ={x -5}/{x+ 5} , x ≠ 5,

then the domain of f–1 (x) is

R
R – (1)
(–α, 1)
(1, α)

Solution:

Explanation: According to the question,

f(x)=\;{x-5}/{x+5}

Let

f(x)=y

y=\;{x-5}/{x+5}

x-5=y x+5 y

x-y x=5 y-5

x(1-y)=5 y+5

x=\;{5 y+5}/{1-y}

f^{-1}(x)=\;{5 x+5}/{1-x}=\;{5(1-x)}/{1-x}

∴ x=1

then domain of

f^{-1}(x)

will be

R-(1)

.

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