How would you solve this?

[struggling_]

I've already figured out that:





I know 'no solutions' means the gradient is the same for both equations, but how would you work it out?

 

[tkhunny]

Have you considered applying the problem statement? [math]f(x) = f^{-1}(x)[/math]

 

[Dr.Peterson]

i don't think the gradient will be involved. "No solutions" just means the values of the two functions are never the same.

Just try solving the equation, see what kind of equation it becomes, and decide how to tell when there are no solution. You won't see what to do at the end until you've done some preliminary work.

 

[HallsofIvy]

\(\displaystyle f(x)= \frac{a}{x- b}\) and, as you have correctly said, \(\displaystyle f^{-1}(x)= \frac{a}{x}+ b\).

So "\(\displaystyle f(x)= f^{1}(x)\)" is \(\displaystyle \frac{a}{x- b}= \frac{a}{x}+ b\).

Solve that equation. Are there any values of a or b that would make that impossible?