Statement 1: If `f(x)` is an odd function, then `f^(prime)(x)` is an even function.

If f(x) is an odd function, then write whether f^(prime)(x) is even or odd.

Statement-1 : If f(x) is a constant function, then f^(-1)(x) is also a constant function. Statement-2 : If graphs of f(x) and f^(-1)(x) are intersecting then they always intersect on the line y = x. Statement-3 : The inverse of f(x) = (x)/(1+|x|) is (x)/(1-|x|)

If f(x) is an even function, then write whether f^(prime)(x) is even or odd.

Statement-1 : f(x) is a one-one function hArr f^(-1) (x) is a one-one function. and Statement-2 f^(-1)(x) is the reflection of the function f(x) with respect to y = x.

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

If f(x) is an odd function, then the curve y=f(x) is symmetric

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? G(x) is an odd function G(x)i s an even function G(x) is neither even nor odd function. Whether G(x) is an odd or even function depends on the value of a

If f:[0,2pi]vec[-1,1]; y=sin x then which of statement is/are true: y=f^(-1)(x) is an odd function y=f^(-1)(x)-pi is an odd function y=f^(-1)(x) is an even function y=f^(-1)(x) is neither even nor odd function

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0