Let f(x) = √x and g (x) = x be two functions

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

$=\frac{\sqrt{x}}{x} \times \frac{\sqrt{x}}{\sqrt{x}}$

$=\frac{\mathrm{X}}{\mathrm{X} \sqrt{\mathrm{X}}}$

$\Rightarrow\left(\frac{f}{g}\right)(x)=\frac{1}{\sqrt{x}}$