Question 511 Mark
Let f(x) = $\sqrt x$ and g(x) = x be two functions defined over the set of non-negative real numbers. Find (f + g) (x), (f – g) (x), (fg) (x) and $\begin{equation} \left(\frac{f}{g}\right)(x) \end{equation}$.
Answer
View full question & answer→We have,
$(f + g) (x)=f(x)+g(x) = $$\sqrt x$ + x,
$(f – g) (x) =f(x)-g(x)= \sqrt x– x,$
$(fg) x = f(x).g(x)=$$ \sqrt{x}(x)=x^{\frac{3}{2}} $
$\left(\frac{f}{g}\right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x}}{x}=x^{-\frac{1}{2}}, x \neq 0 $
$(f + g) (x)=f(x)+g(x) = $$\sqrt x$ + x,
$(f – g) (x) =f(x)-g(x)= \sqrt x– x,$
$(fg) x = f(x).g(x)=$$ \sqrt{x}(x)=x^{\frac{3}{2}} $
$\left(\frac{f}{g}\right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x}}{x}=x^{-\frac{1}{2}}, x \neq 0 $