If `f^(prime)(0)=1AAxandyandf(x+y)=f(x)*f(y)` then `f(1)` is equal to

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^(')(0) exists and equals -1 and f(0) =1, then f^(')(2) is equal to

If y=f(x) satisfies f(x+1)+f(z-1)=f(x+z) AA x, z in R and f(0)=0 and f'(0)=4 then f(2) is equal to

Let f((x+y)/(2))=1/2 |f(x) +f(y)| for all real x and y, if f '(0) exists and equal to (-1), and f(0)=1 then f(2) is equal to-

If f:R rarr R be a function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y and f(2) = 4 then, f(1)-f(0) is equal to