Q13 of 68 Page 27

If f and g are two real valued functions defined as f (x) = 2x + 1, g (x) = x2 + 1, then find.

fg

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


To find: fg


Explanation: this can be obtained by multipying functions f(x) and g(x), i.e.,


So, fg = (fg)(x)


⇒ fg = f(x) g(x)


Substituting the corresponding equation, we get


⇒ fg = (2x + 1)( x2 + 1)


⇒ fg = 2x(x2 ) + 2x(1) + 1(x2) + 1(1)


⇒ fg = 2x3 + 2x + x2 + 1


⇒ fg = 2x3 + x2 + 2x + 1


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