Let f(x) = √x and g (x) = x be two functions defined in the domain R+∪ {0}. Find (i) (fg) (x) (ii) (f/g) (x)

Home » Let f(x) = √x and g (x) = x be two functions defined in the domain R+∪ {0}. Find (i) (fg) (x) (ii) (f/g) (x)

Let f(x) = √x and g (x) = x be two functions defined in the domain R+∪ {0}. Find (i) (fg) (x) (ii) (f/g) (x)

Solution:

(i) $(\mathrm{fg})(\mathrm{x})$

$\Rightarrow(f g)(x)=f(x) g(x)$

$\Rightarrow(f g)(x)=(\sqrt{x})(x)$

$\Rightarrow f(x) g(x)=x \sqrt{x}$

(ii) $(f / q)(x)=f(x) / g(x)$

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

Now multiply and divide by $\sqrt{x}$ ,

We have

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

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

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