Home
Class 12
MATHS
The function f :R -> R satisfies the con...

The function `f :R -> R` satisfies the condition `mf(x - 1) + nf(-x) = 2| x | + 1`. If `f(-2) = 5` and `f(1) = 1` find m+n

Text Solution

Verified by Experts

The correct Answer is:
`4/3`
Promotional Banner

Similar Questions

Explore conceptually related problems

A derivable function f : R^(+) rarr R satisfies the condition f(x) - f(y) ge log((x)/(y)) + x - y, AA x, y in R^(+) . If g denotes the derivative of f, then the value of the sum sum_(n=1)^(100) g((1)/(n)) is

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

A function y = f(x) satisfies the condition f(x+(1)/x) =x^(2)+1/(x^2)(x ne 0) then f(x) = ........

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

For x inR - {1} , the function f(x ) satisfies f(x) + 2f(1/(1-x))=x . Find f(2) .

Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R . Write f^(-1) .

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

If f(x) is a differntiable function satisfying the condition f(100x)=x+f(100x-100), forall x in R and f(100)=1, then f(10^(4)) is