# Find the equation of the inverse function for the following function if f(x)=3x+1 and g(x)=x+2 then find (fg)(x) if f(x)=3x+1 and g(x)=x+2 then find (fg)(x)

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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.

y=3x+1

x=3y+1

3y=x-1

`y=(x-1)/3`

**So `f^(-1)(x)=(x-1)/3` **

** 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:

y=x+2

x=y+2

y=x-2

**So `g^(-1)(x)=x-2` **

(3)Find (fg)(x):

This is simply the product f(x)g(x)

`(fg)(x)=(3x+1)(x+2)=3x^2+7x+2`

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**