Which of the following pairs of functions is/are identical? (a) `f(x)="tan"(tan^(-1)x)a n dg(x)="cot"(cot^(-1)x)` (b)`f(x)=sgn(x)a n dg(x)=sgn(sgn(x))` (c)`f(x)=cot^2xdotcos^2xa n dg(x)=cot^2x-cos^2x` (d)`f(x)=e^(lnsec^(-1)x)a n dg(x)=sec^(-1)x`

f(x)=cot^(2)x*cos^(2)x, g(x)=cot^(2)x-cos^(2)x

Which of the following functions are identical? (a)f(x)=1nx^2a n dg(x)=21nx (b)f(x)=(log)_x ea n dg(x)=1/((log)_e x) (c)f(x)="sin"(cos^(-1)x)a n dg(x)="cos"(sin^(-1)x) (d)non eoft h e s e

Find the values of x for which the following pair of functions are identical. (i) f(x)=tan^(-1)x+cot^(-1)x " and " g(x)=sin^(-1)x +cos^(-1)x (ii) f(x)=cos(cos^(-1)x) " and " g(x)=cos^(-1)(cosx)

f(x)=sgn(cot^(- 1)x),g(x)=sgn(x^2-4x+5)

Find the value of x for which function are identical. f(x)=cosxa n dg(x)=1/(sqrt(1+tan^2x))

Which of the following pairs of functions is NOT identical? (a) e^((lnx)/2) and sqrt(x) (b) tan(tanx) and cot(cotx) (c) cos^(2)x+sin^(4)x and sin^(2)x+cos^(4)x (d) (|x|)/x and sgn(x) where sgn(x) stands for signum function.

Column I: Function, Column II: Value of x for which both the functions in any option of column I are identical f(x)=tan^(-1)((2x)/(1-x^2)),g(x)=2tan^(-1)x , p. x in {-1,1} f(x)=sin^(-1)(sinx)a n dg(x)="sin"(sin^(-1)x) , q. x in [-1,1] f(x)=(log)_(x2)25a n dg(x)=(log)_x5 , r. x in (-1,1) f(x)=sec^(-1)x+cos e c^(-1)x ,g(x)=sin^(-1)x+cos^(-1)x , s. x in (0,1)

For which of the following functions f(0) exists such that f(x) is continuous at x=0 f(x)=1/((log)_e|x|) b. f(x)=(cos((sin|x|)/x)) c. f(x)=x sin(pi/x) d. f(x)=1/(1+2^(cot x))

Find the range of the following (i) f(x)="sgn"(x^(2)) " (ii) "f(x)="sgn"(x^(2)-2x+3)

For the following functions write the piecewise definition and draw the graph (i) f(x)=" sgn "(log_(e)x) " (ii) "f(x) = " sgn "(sin x)