what is the inverse of the given relation?

for the function f(x)=xx-2,find (fof-1)(10)

Not sure just what your f(x) is, but for any inverse function

g(x) = f^-1(x),

(f◦g)(x) = (g◦f)(x) = x

To find the inverse of a given relation, we need to follow these steps:

1. Start with the original function, which in this case is f(x) = x(x - 2).
2. Replace f(x) with y: y = x(x - 2).
3. Swap the variables x and y: x = y(y - 2).
4. Solve the equation for y. Let's expand the equation: x = y^2 - 2y.
5. Rearrange the equation to isolate y: y^2 - 2y - x = 0.
6. This is now a quadratic equation in terms of y. We can solve it using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 1, b = -2, and c = -x.
7. Simplify the equation using the quadratic formula: y = (2 ± √(4 + 4x)) / 2.
8. Further simplify by factoring out 2 from the numerator: y = (1 ± √(1 + x)).

So, the inverse of the given relation f(x) = x(x - 2) is f^(-1)(x) = (1 ± √(1 + x)).

Now, to evaluate (fof^(-1))(10), we need to substitute f^(-1)(x) into f(x).

1. Replace x in f(x) with f^(-1)(x): f(f^(-1)(x)) = (f^(-1)(x))(f^(-1)(x) - 2).
2. Substitute x = 10: f(f^(-1)(10)) = (f^(-1)(10))(f^(-1)(10) - 2).

There is no further calculation possible without the specific value of f^(-1)(10).