Home
Class 12
MATHS
Let f(x) be a real valued function not i...

Let f(x) be a real valued function not identically zero, which satisfied the following conditions
I. `f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y` are any real numbers.
II. `f'(0) ge 0`
The value of f(1), is

A

0

B

1

C

2

D

Not defined

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f(x), is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f'(10), is

f(x) is a real valued function f(x) = (1)/(sqrt(5x-3)) . Find the domain of f(x).

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

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

Let f be real valued function from N to N satisfying. The relation f(m+n)=f(m)+f(n) for all m,n in N . The range of f contains all the even numbers, the value of f(1) is

Let f be a function satisfying of xdot Then f(x y)=(f(x))/y for all positive real numbers xa n dydot If f(30)=20 , then find the value of f(40)dot

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

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} 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