Consider, f (x) is a function such that `f(1)=1, f(2)=4 and f(3)=9`
Statement 1 : `f''(x)=2" for some "x in (1,3)`
Statement 2 : `g(x)=x^(2) rArr g''(x)=2, AA x in R`

Consider the functions f(x)=sqrt(x-2) , g(x)=(x+1)/(x^2-2x+1) Find (f+g)(x)

If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? f'(x)=2AA x in(1,3)f'(x)=f(x)=5 for some x in(2,3)f'(x)=3AA x in(2,3)f'(x)=2 for some x in(1,3)

Let f_(1):R rarr R and f_(2):C rarr C are two functions such that f_(1)(x)=x^(3) and f_(2)=x^(3) .Prove that f_(1) and f_(2) are not same.

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

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