+118673 if f(x)=2x/x-5,
find f^-1(x).
That is a bit better :)
You have written
\(if\\ f(x)=\frac{2x}{x}-5\\ find \;\;f^{-1}(x).\)
But I expect you left out the brackets and you actually mean
\(if\\ f(x)=\frac{2x}{x-5}\\ find \;\;f^{-1}(x).\)
Be careful with those brackets.
Let
\(y=\frac{2x}{x-5}\\ \text{x cannot be 5}\\ \text{Now make x the subject}\\ yx-5y=2x\\ yx-2x=5y\\ x(y-2)=5y\\ x=\frac{5y}{y-2}\\ \text{Now for the inverse swap x and y over}\\ y=\frac{5x}{x-2} \)
So if
\(f(x)=\frac{2x}{x-5}\\then\\ f^{-1}(x)=\frac{5x}{x-2}\\ where\;\;x\ne2\)
Here are the graphs
The inverse fof a funtion is the reflection of the funtion in the line y=x
NOW LEARN FROM THIS AND TRY AND DO THE REST BY YOURSELF!
