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`

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

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 function is (are) even, odd, or neither? (a). f(x)=x^2sinx (b). f(x)=log((1-x)/(1+x)) (c). f(x)=log(x+sqrt(1+x^2)) (d). f(x)=(e^x+e^(-x))/2

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

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 domain of the following following functions: (a) f(x)=(sin^(-1))/(x) (b) f(x)=sin^(-1)(|x-1|-2) (c ) f(x)=cos^(-1)(1+3x+2x^(2)) (d ) f(x)=(sin^(-1)(x-3))/(sqrt(9-x^(2))) (e ) f(x)="cos"^(-1)((6-3x)/(4))+"cosec"^(-1)((x-1)/(2)) (f) f(x)=sqrt("sec"^(-1)((2-|x|)/(4)))

Let f: RvecR and g: Rvec be two functions such that fog(x)=sinx^2a n d gof(x)= sin^2x dot Then, find f(x)a n dg(x)dot

f(x)=log_(e)x, g(x)=1/(log_(x)e) . Identical function or not?

Find the cosine of the angle of intersection of curves f(x)=2^x(log)_e xa n dg(x)=x^(2x)-1.