SOLUTION: I could use some help on this problem, anything is helpful! f(x) = 6x − 2 show that the given function is one-to-one and find its inverse. Check your answers algebrai

Algebra ->  Functions -> SOLUTION: I could use some help on this problem, anything is helpful! f(x) = 6x − 2 show that the given function is one-to-one and find its inverse. Check your answers algebrai      Log On


   

Question 1039152: I could use some help on this problem, anything is helpful!
f(x) = 6x − 2
show that the given function is one-to-one and find its inverse. Check your
answers algebraically and graphically. Verify that the range of f is the domain of f^−1 and vice-versa.
Please help! I really appreciate it!
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C6x-2%2C%28x%2B2%29%2F6%29
This passes the horizontal and vertical line tests and is one-to-one.
To do the inverse of a function, change the x and y, and if there is an inverse, it will be symmetric around the y=x line. You can reflect the function across the 45 degree line and can see that in the graph.
For a function f(x)=6x-2
y=6x-2
now change the x and y
x=6y-2
Solve for y
x+2=6y
divide by 6
(x+2)/6=y
The inverse is
x=6y-2
y=(x+2)/6
The range of the first function is infinite and so is the domain of the second.
The range of the second function is also infinite, and so is its domain.