Let `F:[3,infty]to[1,infty]` be defined by `f(x)=pi^(x(x-3)`, if `f^(-1)(x)` is inverse of `f(x)` then the number of solution of the equation `f(x)=f^(-1)(x)` are

Answer

1

Explanation

`f(x)=pi^(x(x-3)):[3,infty]to[1,infty]`
solution of `f(x)=f^(-1)(x)` lies on line `y=x`
for `x in [3,infty]` the function
`f(x)=pi^(x(x-3))` is strictly increasing and intersect the line y
`=x` at only one point
`f(x)=f^(-1)(x)` has only one solution