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$Let f (x) = \frac{9^{x}}{9^{x} + 3} . Then f (x) + f (1 - x) =$

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b

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d

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detailed solution

Correct option is B

fx+f1-x = 9x9x+3 +91-x91-x+3 =9x9x+3+99x99x+3 =9x9x+3+99+3·9x =9x9x+3+33+9x=9x+39x+3 =1

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$Let f (x) = ({[a]}^{2} - 5 [a] + 4) x^{3} - (6 {\{a\}}^{2} - 5 \{a\} + 1) x - (\tan x) (s g n x)$ be an even function for all $x \in R .$ Then the sum of all possible values of a is (where [.] and {.} denote greatest integer function and fractional part function, respectively)

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