Question

Consider this function. f(x) = 2x - 2 Which graph represents the inverse of function f?

Answer 1

Inverse of function $f(x)=2x-2$ is $f^{-1}(x)=\frac{x}{2} +1$

Since Options are not available, compare the graphs of figure attached with your options.

Step-by-step explanation:

The function given is: f(x)=2x-2

We need to find the graph of inverse of this function.

Finding inverse of f(x)=2x-2

Let y=2x-2

Interchange the positions of x and y

$x=2y-2$

Now solve for y:

Adding 2 on both sides

$x+2=2y-2+2\\x+2=2y$

Divide both sides by 2

$\frac{x+2}{2}=y\\\frac{x}{2} +1=y$

Replace y by f^{-1}

$f^{-1}(x)=\frac{x}{2} +1$

SO, Inverse of function $f(x)=2x-2$ is $f^{-1}(x)=\frac{x}{2} +1$

The graphs are attached in figure below.

Since Options are not available, compare the graphs of figure attached with your options.

Keywords: Inverse of Function

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