Given f(x)=3x+1, g(x)=x+2:
(1) The inverse of f(x) can be found by switching "x" and "y" and then solving for y.
** Note that in f(x) you multiply the input by 3 and then add 1 to the result. In the inverse, you subtract 1 from the input , then divide by 3. You perform the inverse operations in the reverse order.
(2) The inverse of g(x) is found in a similar manner:
This is simply the product f(x)g(x)
Given -> f(x)=(3x+1) and g(x)=(x+2)
Require to find -> fg(x)
fg(x) = f(x)*g(x)
=> fg(x) = (3x+1)(x+2)
=> fg(x) =3(x^2)+6x+x+2
=> fg(x) = 3x^2+7x+2
hence, fg(x)=3x^2 + 7x + 2 --> Answer