Let `g(x)` be the inverse of an invertible function `f(x)` which is differentiable at `x=c` . Then `g^(prime)(f(x))` equal. (a)`f^(prime)(c)` (b) `1/(f^(prime)(c))` (c) `f(c)` (d) none of these

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g^('')(f(x)) equals. (a) -(f^('')(x))/((f^'(x))^3) (b) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^3)/(f^(prime)(x)) (c) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2) (d) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

If g is the inverse of a function f and f'(x)=(1)/(1+x^(5)) , then g'(x) is equal to-

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _

Let f(x y)=f(x)f(y)AAx , y in R and f is differentiable at x=1 such that f^(prime)(1)=1. Also, f(1)!=0,f(2)=3. Then find f^(prime)(2)

If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i equal to :

Let y=f(x) be a parabola, having its axis parallel to the y-axis, which is touched by the line y=x at x=1. Then, (a) 2f(0)=1-f^(prime)(0) (b) f(0)+f^(prime)(0)+f(0)=1 (c) f^(prime)(1)=1 (d) f^(prime)(0)=f^(prime)(1)

If f is a continuous function on [0,1], differentiable in (0, 1) such that f(1)=0, then there exists some c in (0,1) such that a) cf^(prime)(c)-f(c)=0 b) cf^(prime)(c)+cf(c)=0 c) f^(prime)(c)-cf(c)=0 d) cf^(prime)(c)+f(c)=0

If f: R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) none of these

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)=|f(x)| (d) none of these