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Question

A function f:[12,)[34,) defined as, f(x)=x2x+1.


Then for what value of x does equation f(x)=f1(x) hold right.

A
x=3
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B
x=2
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C
x=1
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D
None of these
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Solution

The correct option is C x=1
f(x)=x2x+1
Substitute f(x)=y
y=x2x+1
x2x+1y=0
x=1±4y32
f1(y)=1±4y32
f1(x)=1±4x32
Now, we will check which value of x from the options gives f(x)=f1(x)
Here, f(3)=7
f1(3)=1±32=2,1
f(x)f1(x) for x=3
Similarly for x=2, f(x)f1(x)
Now, for x=1
f(1)=1
f1=1±12=1,0
Hence, for x=1 , f(x)=f1(x)

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