# Math Help - Stuck on inverting a function

1. ## Stuck on inverting a function

$f(x)=0.5+\frac{5}{0.2x}$ $,x\neq0$

I'm having some difficulty on finding the inverse function for this problem.

I follow the first method of switching the 'x' and 'y' variables and then subtracting the $0.5$ from both sides, $x-0.5=\frac{5}{0.2y}$. Here's where my intuition breaks down. I know the objective is to solve for 'y'. Thus, multiply '0.2y' on both sides? $0.2y(x-0.5)=5$.

Should I divide by $(x-0.5)$? That would give me $0.2y=\frac{5}{x-0.5}$

And then divide $0.2$ from both sides and I end up with $y=\frac{1}{x-0.5}$

I've tried working some inputs and the function is definitely not the inverse function, so I know my math is wrong. If somebody could toss me a tip I would appreciate it.

2. ## Re: Stuck on inverting a function

Originally Posted by AZach
$f(x)=0.5+\frac{5}{0.2x}$ $,x\neq0$

I'm having some difficulty on finding the inverse function for this problem.

I follow the first method of switching the 'x' and 'y' variables and then subtracting the $0.5$ from both sides, $x-0.5=\frac{5}{0.2y}$. Here's where my intuition breaks down. I know the objective is to solve for 'y'. Thus, multiply '0.2y' on both sides? $0.2y(x-0.5)=5$.

Should I divide by $(x-0.5)$? That would give me $0.2y=\frac{5}{x-0.5}$

And then divide $0.2$ from both sides and I end up with $y=\frac{1}{x-0.5}$

5 divided by 0.2 is 25, not 1
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