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)
2 Answers
embizze | High School Teacher | (Level 2) Educator Emeritus
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`
vaaruni | High School Teacher | (Level 1) Salutatorian
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