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

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)=√(x) \ \ \ for \ x >= 0`

intersection point are for x >= 0

`x^2=√(x) <=>x^4=x<=>x^3=1 \ or \ x=0<=> x = 1 \ or \ x=0`

hope this helps

Answer 2

D

Explanation: