If f and g are two real valued functions

Solution:

According to the question,

f and g be real valued functions defined as f (x) = 2x + 1, g (x) = x2 + 1,

(i) f + g

⇒ f + g = f(x) + g(x)

= 2x + 1 + x2 + 1

= x2 + 2x + 2

(ii) f – g

⇒ f – g = f(x) – g(x)

= 2x + 1 – (x2 + 1)

= 2x – x2

(iii) fg

⇒ fg = f(x) g(x)

= (2x + 1)( x2 + 1)

= 2x(x2 ) + 2x(1) + 1(x2) + 1(1)

= 2x3 + 2x + x2 + 1

= 2x3 + x2 + 2x + 1

(iv) f/g

f/g = f(x)/g(x)

$\Rightarrow \frac{f}{g}=\frac{(2 x+1)}{x^{2}+1}$