Question:
Let f(x) = √x and g (x) = x be two functions defined in the domain R+∪ {0}. Find
(i) (f + g) (x)
(ii) (f – g) (x)
(iii) (fg) (x)
(iv) (f/g) (x)
Solution:
(i)
(f + g)(x)
⇒ (f + g)(x) = f(x) + g(x)
⇒ f(x) + g(x) = √x + x
(ii)
(f – g)(x)
⇒ (f – g)(x) = f(x) – g(x)
⇒ f(x) – g(x) = √x–x
(iii)
(fg)(x)
⇒ (fg)(x) = f(x) g(x)
⇒ (fg)(x) = (√x)(x)
⇒ f(x)g(x)= x√x
(iv)
(f/q)(x) = f(x)/g(x)
$\Rightarrow\left(\frac{f}{g}\right)(x)=\frac{\sqrt{x}}{x}$
Multiplying and dividing by $\sqrt{x}$, We get
$=\frac{\sqrt{x}}{x} \times \frac{\sqrt{x}}{\sqrt{x}}$
$=\frac{\mathrm{X}}{\mathrm{X} \sqrt{\mathrm{X}}}$
$\Rightarrow\left(\frac{f}{g}\right)(x)=\frac{1}{\sqrt{x}}$