How do you find the inverse of f(x) = (2x-1)/(x-1) and is it a function?
1 Answer
May 14, 2016
f^-1(x)=(-x+1)/(2-x) - yes, it is a function
Explanation:
Determining the Inverse Function
Given,
f(x)=(2x-1)/(x-1)
Substitute
y=(2x-1)/(x-1)
Swap the
x=(2y-1)/(y-1)
Solve for
x(y-1)=2y-1
xy-x=2y-1
2y-xy=-x+1
Factor out
y(2-x)=-x+1
y=(-x+1)/(2-x)
Rewrite
color(green)(|bar(ul(color(white)(a/a)color(black)(f^-1(x)=(-x+1)/(2-x))color(white)(a/a)|)))
Determining Whether the Inverse Function Is a Function
Graphically,
graph{(-x+1)/(2-x) [-10, 10, -5, 5]}
In the graph above, you can see that the
:. , the inverse function is a function.