LimitsHard
Question
If f(x) is a continuous function for all real values of x satisfying x2 + (f(x) - 2)x + 2√3 - 3 - √3 f(x) = 0, then the value of f(√3) is -
Options
A.√3
B.1 - √3
C.2(1 - √3)
D.2(√3 - 1)
Solution
As f(x) is continuous for all x ∈ R
Thus
f(x) = f(√3)
since f(x) =
,x ≠ √3
∴
f(x) = 
= 2(1 - √3)
Thus f(√3) = 2(1 - √3)
Thus
f(x) = f(√3)since f(x) =
,x ≠ √3∴
f(x) = = 2(1 - √3)Thus f(√3) = 2(1 - √3)
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