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Question

If f is an even function defined on the interval (5,5) then find the total number of real value of x satisfying the equations f(x)=f(x+1x+2) are

A
1
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B
2
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C
4
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D
8
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Solution

The correct option is A 2
If f(x) is an even function in x(5,5)
f(x)=f(x)
then f(x)=f(x+1x+2) can be written
as f(x)=f(1x2x)

By putting x=x
x=1x2x
2xx2=1x
x2+13x=0
x=3±52

Therefore, two real values of x.

Hence, this is the answer.

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