Question
The function f(x) satisfies the equation (x- 1)f(x) + f(1x) = 1, for all x not equal to zero. The value of f(99) is
Answer: Option C
:
C
Substituting x = 99 gives 98f(99) + f(199)=1 and substituting x = 199 gives -9899 f(199) + f(99) = 1.98
times of the first equation plus 99 times of the second equation simplify to 9703×f(99)=197;
f(99) = 1979703 . Option (c).
Substituting x = 99 gives 98
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:
C
Substituting x = 99 gives 98f(99) + f(199)=1 and substituting x = 199 gives -9899 f(199) + f(99) = 1.98
times of the first equation plus 99 times of the second equation simplify to 9703×f(99)=197;
f(99) = 1979703 . Option (c).
Substituting x = 99 gives 98
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