The number of points at which `g(x)=1/(1+2/(f(x)))` is not differentiable, where `f(x)=1/(1+1/x)` , is `1` b. `2` c. `3` d. `4`

If f (x) =(1)/(x +1) then its differentiate is given by :

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lt=xlt=2 3-x ,2 2

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

If f(x)=x^2 and is differentiable an [1,2] f'(c) at c where c in [1,2]:

The values of ba n dc for which the identity of f(x+1)-f(x)=8x+3 is satisfied, where f(x)=b x^2+c x+d ,a r e b=2,c=1 (b) b=4,c=-1 b=-1, c=4 (d) b=-1,c=1

If f: R->Q (rational numbers), g: R->Q (Rational number ) are two continuous functions such that sqrt(3)f(x)+g(x)=4, then (1-f(x))^3+(g(x)-3)^3 is equal to a. 1 b. 2 c. 3 d. 4

Let f(x)=2x+1. Then the number of real number of real values of x for which the three unequal numbers f(x),f(2x),f(4x) are in G.P. is 1 b. 2 c. 0 d. none of these

If f(x+1/2)+f(x-1/2)=f(x) for all x in R , then the period of f(x) is 1 (b) 2 (c) 3 (d) 4

f is a strictly monotonic differentiable function with f^(prime)(x)=1/(sqrt(1+x^3))dot If g is the inverse of f, then g^(x)= a. (2x^2)/(2sqrt(1+x^3)) b. (2g^2(x))/(2sqrt(1+g^2(x))) c. 3/2g^2(x) d. (x^2)/(sqrt(1+x^3))