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Suppose that a function f : R to R s...

Suppose that a function `f : R to R ` satisfies `f(x + y) = f(x) f(y)` for all x `y in R ` and `f(1) = 3` . If `underset(i=l)overset(n)sum f(i) = 363`, then n is equa to _______ .

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Knowledge Check

  • If f:RtoR satisfies f(x+y)=f(x)+f(y) for all x,y in R and f(1)=7, then sum_(r=1)^(n) f(r) , is

    A
    `3^(m)-1`
    B
    `3^(m)`
    C
    `3^(m-1)`
    D
    none of these

  • If f : R rarr R satisfies f(x + y) = f(x) + f(y) x, y in R and f(1) = 7, then sum_(r = 1)^(n) f(r) =

    A
    `(7n)/(2)`
    B
    `(7 (n + 1))/(2)`
    C
    `7n (n + 1)`
    D
    `(7n (n + 1))/(2)`

  • Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

    A
    f(x) an even function , if `f(0) ne 0`
    B
    f(x) is an odd function, if `f(0) ne 0`
    C
    f(x) an even function , if `f(0)=0`
    D
    f(x) is an odd function , if `f(0)=0`

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