[" (i) "f(x)=(2x+3)/(x-2)],[" (ii) "f(x)=x+(1)/(x)]

Find the domains and ranges of the real valued functions: (i) f(x) =1/(2x+1) , (ii) f(x) = (2+x)/(2-x) (iii) f(x) =x/(2-3x)

Find domain(i) f(x) = (1)/(x - 5) (ii) f(x) = (3 - x)/(x - 3) (iii) f(x) = (x^(2) - 1)/(x - 1) (iv) f(x) = (| x - 3 |)/(x - 3) (v) f(x) = (1)/(2 - sin 3x)

If f(x)=(2x+3)/(x-2) , then: (f@f)(x)=

(i) f(x) = sqrt(3 - 2x) (ii) f(x) = (1)/(sqrt(x + 2)) (iii) f(x) = 1 + x - [x - 2] . Find the domain of the following (23 - 24) :

Draw the graph of the exponential funcation. (i) f(x) = 2^(x) (ii) f(x) = (1/3)^(x)

Discuss continuity of (i) f(x) = sgn(x^(3)-x) (ii) f(x) = sgn(2 cos x-1) (iii) f(x) = sgn(x^(2)-2x+3)

If f(x)=a^x, which of the following equalities do not hold ? (i) f(x+2)-2f(x+1)+f(x)=(a-1)^2f(x) (ii) f(-x)f(x)-1=0 (iii) f(x+y)=f(x)f(y) (iv) f(x+3)-2f(x+2)+f(x+1)=(a-2)^2f(x+1)

If f(x)=a^x, which of the following equalities do not hold ? (i) f(x+2)-2f(x+1)+f(x)=(a-1)^2f(x) (ii) f(-x)f(x)-1=0 (iii) f(x+y)=f(x)f(y) (iv) f(x+3)-2f(x+2)+f(x+1)=(a-2)^2f(x+1)

If f(x)="cos"^(2)x+"sec"^(2)x , then (i) f(x)lt1 (ii) f(x)=1 (iii) 2ltf(x)lt1 (iv) f(x)ge2

Discuss the applicability of Rolle's theorem to the functions : (i) f(x) = x^(2) "in " [1, 2] (ii) f(x) = x^(2//3) " in " [-1, 1]