If `x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1.` prove that: `1+a b+a^2b^2+oo=(x y)/(x+y-1)`

Find the inverse of the function: f:(-oo,1] rarr [1/2,oo],w h e r ef(x)=2^(x(x-2))

Find the inverse of the function: f:[1, oo) rarr [1,oo),w h e r ef(x)=2^(x(x-2))

Find the inverse of the function: f:[1, oo) rarr [1,oo),w h e r ef(x)=2^(x(x-2))

Evaluate the following integral: int_2^4f(x)dx ,\ w h e r e\f(x)={7x+3,\ if\ 1lt=xlt=3 , w h e r e\f(x)=8x \ if\ 3lt=xlt=4

The domain of f(x)=1n(a x^3+(a+b)x^2+(b+c)x+c), where a >0,b^2-4a c=0,i s(w h e r e[dot] represetns greatest integer function). (-1,oo)~(-b/(2a)) (1, oo)~{-b/(2a)} (-1,1)~{-b/(2a)} non eoft h e s e

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to -2 (b) -1 z e ro (d) none of these

If z=(i)^((i)^(i)) w h e r e i=sqrt(-1),t h e n|z| is equal to a. 1 b. e^(-pi//2) c. e^(-pi) d. none of these

Discuss monotonocity of f(x)=x/(sinx)a n d g(x)= x / (tanx), w h e r e

Find the domain and range of f(x)=log{x},w h e r e{} represents the fractional part function).

Find the domain and range of f(x)=log{x},w h e r e{} represents the fractional part function).