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

##### 1 Answer

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#### Explanation

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#### 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.

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