True or False Math Question?

If the inverse of a function f(x) exists, then the y-intercept of f(x) is the x-intercept of its inverse.





True of false??True or False Math Question?
True.





In the case of a first-order function:


y(x) = mx + b


the inverse is y^(-1)(x) = (x-b)/m.


the y intercept of the original is b.


the x intercept of the inverse is where f^(-1)(x) equals zero. So that means (x-b)/m equals zero. For this to happen, x has to equal b. So. y intercept of original = b. x-intercept of inverse = b. And so the two intercepts are always going to be the same.