The inverse of the function is : [tex]\frac{-1-6x}{2x}[/tex]
What is an inverse function?
An inverse function is a function that serves as an eliminator of a given function.
A function that has an inverse is called invertible function and it is denoted as [tex]f^{-1}[/tex].
Analysis:
let y = [tex]\frac{-1}{2(x+3)}[/tex]
so that,
2y(x+3) = -1
2yx + 6y = -1
2yx = -1 -6
x = [tex]\frac{-1 - 6y}{2y}[/tex]
replacing y with x
[tex]f^{-1}[/tex](x) = [tex]\frac{-1-6x}{2x}[/tex]
In conclusion, the inverse of the function is : [tex]\frac{-1-6x}{2x}[/tex]
Learn more about inverse functions: brainly.com/question/3831584
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