Answer:
Step-by-step explanation:
Hello,
there is not always an intersection point
let's take the example of on the appropriate domain
[tex]f(x)=e^x \ \ \ f^{-1}(x)=ln(x)[/tex]
there is no intersection point
if there is one it means that the point (x,f(x)) and the point (x,[tex]f^{-1}(x)[/tex]) is the same so that have to solve
[tex]f(x)=f^{-1}(x)[/tex]
for instance if we take
[tex]f(x)=x^2 \ \ \ f^{-1}(x)=\sqrt{x} \ \ \ for \ x >= 0[/tex]
intersection point are for x >= 0
[tex]x^2=\sqrt{x} <=>x^4=x<=>x^3=1 \ or \ x=0<=> x = 1 \ or \ x=0[/tex]
hope this helps
