Question

The function: f^-1(x)=2x/2+3xis the function 1-1? if it is find the inverse

Answer 1

`y=(2x)/(2-3x)`

1) The best way to tackle this question is by plotting the graph of this function and then performing the horizontal line test.

So let's sketch out the following function:

Note that this function is a one-to-one function for a horizontal line hits the graph only once.

2) Since, invertible functions can only come from Bijective functions (one-to-one and surjective functions simultaneously) then we can write out this and find the inverse of that inverse function, swapping the variables and then isolating the x on the left side

`\begin{gathered} y=(2x)/(2+3x) \\ x=(2y)/(2+3y) \\ 2y=(2+3y)x \\ 2y=2x+3yx \\ -3yx+2y=2x \\ y(-3x+2)=2x \\ (y(-3x+2))/((-3x+2))=(2x)/((-3x+2)) \\ y=(2x)/(2-3x) \\ \end{gathered}`