Which of the following functions is/are bounded ? `f(x)=(2x)/(1+x^2), [-2,2]`

Find which of the following functions is even or odd ? f(x)=log(x+sqrt(1+x^2))

Which of the following functions is the inverse of itself? (a) f(x)=(1-x)/(1+x) (b) f(x)=5^(logx) (c) f(x)=2(x(x-1)) (d) None of these

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number

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

Which of the following functions is (are) even, odd, or neither ? (i) f(x)=x^(2)sinx " (ii) " f(x)=sqrt(1+x+x^(2))-sqrt(1-x+x^(2)) (iii) f(x)=log((1-x)/(1+x)) " (iv) " f(x)=log(x+sqrt(1+x^(2))) (v) f(x)=sinx-cosx " (vi) " f(x)=(e^(x)+e^(-x))/(2)

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Find the values of x for which the following function is defined: f(x)=sqrt((1)/(|x-2|-(x-2)))

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 ;0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 ;0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

Find the values of x for which the following functions are identical. (i) f(x)=x " and " g(x)=(1)/(1//x) (ii) f(x)=(sqrt(9-x^(2)))/(sqrt(x-2)) " and " g(x)=sqrt((9-x^(2))/(x-2))

Find the domain of definitions of each of the following functions : f(x)=(x+2)/sqrt(x^2-x-2)