Question:
If f and g are two real valued functions defined as f (x) = 2x + 1, g (x) = x2 + 1, then find.
(i) f + g
(ii) f – g
(iii) fg
(iv)f/g
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)
$\Rightarrow \frac{f}{g}=\frac{(2 x+1)}{x^{2}+1}$