Question

If f(x) and it’s inverse function, f^-1(x), are, both plotted on the same coordinate plane, what is their point of intersection

Answer 1

Answer:

Step-by-step explanation:

Hello,

there is not always an intersection point

let's take the example of on the appropriate domain

$f(x)=e^x \ \ \ f^{-1}(x)=ln(x)$

there is no intersection point

if there is one it means that the point (x,f(x)) and the point (x,$f^{-1}(x)$) is the same so that have to solve

$f(x)=f^{-1}(x)$

for instance if we take

$f(x)=x^2 \ \ \ f^{-1}(x)=\sqrt{x} \ \ \ for \ x >= 0$

intersection point are for x >= 0

$x^2=\sqrt{x} x^4=xx^3=1 \ or \ x=0 x = 1 \ or \ x=0$

hope this helps