SOLUTION: f(x)=3x^2-x+10 g(x)=1-20x Find find the inverse of both functions

Question 483734: f(x)=3x^2-x+10
g(x)=1-20x
Find find the inverse of both functions
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
f(x)=3x^2-x+10
g(x)=1-20x
Find find the inverse of both functions
**
The procedure for finding the inverse of a function is to interchange x and y, then solve for y. In effect, you are solving x in terms of y.
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f(x)=3x^2-x+10
y=3x^2-x+10
interchange x and y
x=3y^2-y+10
3y^2-y+10=x
complete the square
3(y^2-y/3+1/36)+10-1/12=x
3(y-1/6)^2+120/12-1/12=x
3(y-1/6)^2+119/12=x
(y-1/6)^2=(x-119/12)/3
(y-1/6)=�((x-119/12)/3)^.5
y=�((x-119/12)/3)^.5+1/6 (This is the inverse of f(x))
As seen by the graph below, f(x) and its inverse are parabolas
..

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g(x)=1-20x
y=1-20x
x=1-20y
20y=1-x
y=(1-x)/20 (This is the inverse of g(x))
see the graph below:
..

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