Start with ##y = \frac x {1 + x}##jimjames said:
I'm not sure what you did here.jimjames said:
The above doesn't help you with this problem. All you're doing is manipulating symbols.jimjames said:
In the line above, all you did was switch x and y.jimjames said:
How did you get the equation above?jimjames said:
Start with y = ##\frac x {1 + x}##jimjames said:
OK.jimjames said:
That's the function you're trying to find the inverse of.jimjames said:
jimjames said:
It's probably simpler to expand y(1 + x), get all terms that involve x on one side, and then isolate x.SammyS said:
jimjames said:
I changed the title a while ago for that very reason.Ray Vickson said:
Subtract xy from both sides: y- xy= y(1-x)= xjimjames said:
To find the inverse for f(x), you need to follow a few steps. First, replace f(x) with y. Then, switch the x and y variables. Next, solve for y. Finally, replace y with f^-1(x) to get the inverse function.
Yes, the inverse of f(x) can be simplified. After switching the x and y variables and solving for y, you may need to use algebraic manipulation to simplify the expression. However, the resulting function will still be the inverse of f(x).
To graph the inverse of f(x), you can use the original function's graph and reflect it over the line y=x. This means that the x and y coordinates will switch places. Additionally, the inverse function will have the same shape as the original function, but it will be a mirror image.
Yes, the inverse of f(x) is a one-to-one function. This means that each input has only one output and each output has only one input. This property is necessary for a function to have an inverse.
You can use the inverse of f(x) to solve equations by plugging in the value of x into the inverse function and solving for y. This will give you the solution to the equation. Additionally, you can use the inverse function to check if a given solution is correct by plugging it into the original function and seeing if it equals the given value of x.