SOLUTION: Find the inverse of the following functions: f(x)=3x-1 I also have to work out f(x)= x+3/2x The problem is, I can't find the formula to work these out anywhere. Pl

Algebra ->  Inverses -> SOLUTION: Find the inverse of the following functions: f(x)=3x-1 I also have to work out f(x)= x+3/2x The problem is, I can't find the formula to work these out anywhere. Pl      Log On


   

Question 163289: Find the inverse of the following functions:
f(x)=3x-1
I also have to work out
f(x)= x+3/2x
The problem is, I can't find the formula to work these out anywhere.
Please help!
Found 2 solutions by Fombitz, KnightOwlTutor:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First, put your function in terms of x and y.
y=3x-1
Now interchange x and y, then solve for y.
highlight%28x%29=3%2Ahighlight%28y%29-1
3y=x%2B1
y=%28x%2B1%29%2F3
That's the inverse of the original function.
f%5E%28-1%29%28x%29=%28x%2B1%29%2F3
.
.
.
y=%28x%2B3%29%2F2x
highlight%28x%29=%28highlight%28y%29%2B3%29%2F%282%2Ahighlight%28y%29%29
2xy=y%2B3
2xy-y=3
y%282x-1%29=3
y=3%2F%282x-1%29
f%5E%28-1%29%28x%29=3%2F%282x-1%29

Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
The first step is to replace f(x) with y and then switch the y and the x and solve
y=3x-1 isolate for the x variable
add 1 to both sides
y+1=3x
Divide both sides by 3
1/3y+1/3=x This is the inverse function
y=x+3/2x
Simplify this equation
2/2x=1x
2/2+3/2=5/2x
Multiply both sides by 2
2y=5x
Divide both sides by 5
2/5y=x