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`

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)

tan^(-1) (cot x) +cot^(-1)(tan x) =pi -2x

Which of the following pairs of function/functions has same graph? y=tan(cos^(-1)x); y=(sqrt(1-x^2))/x y=t a n(cot^(-1)x);y=1/x y="sin"(tan^(-1)x); y=x/(sqrt(1+x^2)) y="cos"(tan^(-1)x); y=sin(cot^(-1)x)

tan ^(-1) (cot x) + cot ^(-1) (tan x) =(pi)/(4)

Discuss the differentiability of f(x)="max"{tan^(-1)x ,cot^(-1)x}dot

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)

If intsqrt(cos e cx+1)dx=kfog(x)+c ,w h e r ek is a real constant, then (a) k=-2,f(x)=cot^(-1)x ,g(x)=sqrt(cos e cx-1) (b) k=-2,f(x)=tan^(-1)x ,g(x)=sqrt(cos e cx-1) (c) k=2,f(x)=tan^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1)) (d) k=2,f(x)=cot^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1))