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Question

If f(x)+2f(1x)=3x,x0 and S={xR:f(x)=f(x)}, then S:
  1. contains exactly one element.
  2. is an empty set.
  3. contains exactly two elements.
  4. contains more than two elements.

A
contains exactly two elements.
B
contains more than two elements.
C
is an empty set.
D
contains exactly one element.
Solution
Verified by Toppr

f(x)+2f(1x)=3x

Putting x as 1x then f(1x)+2f(x)=3x

Solving these two equations,
f(x)=2xx

Now for f(x)=f(x)

2xx=x2x

2×2x=2x

x2=2

x=2,2

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