If the following functions are defined from `[-1,1]to[-1,1],` select those which are not bijective. (a)`sin(sin^(-1)x)` (b) `2/pisin^(-1)(sinx)` (c)`(sgn(x))ln(e^x)` (d) `x^3(sgn(x))`

sgn(x^(2)-1)=(x+1)^(2)

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

Differentiate the following functions with respect to x:(e^(x)+sin x)/(1+log x)

The range of the function f(x)=sgn((sin^(2)x+2sin x+4)/(sin^(2)x+2sin x+3)) is

Find the inverse of the function f: [-1,1] to [-1,1],f(x) =x^(2) xx sgn (x).

int_(-1)^(3)sgn(x-[x])dx

The domain of the function f(x)=sin^(-1)""(1)/abs(x^(2)-1)+1/sqrt(sin^(2)x+sinx+1) is

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)

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? f(x)=1nx^(2) and g(x)=2ln xf(x)=log_(x)e and g(x)=(1)/(log x)f(x)=sin(cos^(-1)x) and g(x)=cos(sin^(-1)x) none of these