How do you find the inverse of # f(x) = (2x-1)/(x-1)# and is it a function?
1 Answer
#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.