Let `f: R ,vecRw h e r ef(x)=(x^2+4x+7)/(x^2+x+1)` . Is `f(x)on eon e ?`

Let f: R to R be defined by f(x)=(x)/(1+x^(2)), x in R. Then, the range of f is (A) [-(1)/(2),(1)/(2)] (B) (-1,1)-{0} (C) R-[-(1)/(2),(1)/(2)] (D) R-[-1,1]

Let f: RrarrR be defined by f(x)=(e^x-e^(-x))//2dot Is f(x) invertible? If so, find is inverse.

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

Let f:R to R be defined by f(x) =e^(x)-e^(-x). Prove that f(x) is invertible. Also find the inverse function.

Let A=R-{3},B=R-{1}, and let f: AvecB be defined by f(x)=(x-2)/(x-3) is f invertible? Explain.

Let f: R to R be defined as f(x) = e^("sgn "x)+ e^(x^(2)) . Then find the range of the function, and also indentify the type of the function : one-one or many-one.

Let f : R to R to given by f(x) = (3 -x^(3))^((1)/(3)) . Then of (x) is

Let f:R->[1,oo) be defined as f(x)=log_10(sqrt(3x^2-4x+k+1)+10) If f(x) is surjective then k =

Let f:R rarr R, f(x)=x+log_(e)(1+x^(2)) . Then