Question

Let `f(x)=sqrt(x)`and `g(x) = x`be two functions defined over the set of nonnegative real numbers. Find `(f + g) (x)`, `(f g) (x)`, `(fg) (x)`and `(f/g)(x)`.

Answer 1

We have `f(x )=sqrt(x) and g(x) =x` be two function defined in the domain `R^(+)uu{0}`
(i) `(f+g)(x)=f(x)+g(x)=sqrt(x)+x " "` (ii) `(f-g)(x)=f(x)-g(x)=sqrt(x)-x`
(iii) `(fg)(x)=f(x)*g(x)=sqrt(x)*x=x^(2/3) " "` (iv) `((f)/(g))(x)=(f(x))/(g(x))=(sqrt(x))/(x)=(1)/(sqrt(x))`