If `f:[-5,5] rarr R` is a differentiable function and if `f'(x)` does not vanish anywhere, then prove that `f(-5) ne f(5)`

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

Let f(x) be a differentiable function and f'(4) = 5, then: underset(xrarr2)lim(f(4)-f(x^2))/(x-2) equals:

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x) = 2ax

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

If f :Rrarr R defined by f(x)= (5x+6)/7 is an invertible function, find f^(-1) .

If: f : R rarr R defined by f(x)= (2x+3)/4 is an invertible function, find f^(-1)

If f: R rarr R defined by f(x) = (3x+5)/2 is an invertible function, find f^-1

Function f : R rarr R f(x) = 3 x -5 is