Question

if the equation of f(x) goes through (1,4) and (4,6), what points does f^(-1)(x) go through? (1,4) and (4,6) (4,1) and (6,4)

Answer 1

If the original function passes through the points (1,4) and (4,6), then the inverse function will pass through the points (4,1) and (6,4).

Step-by-step explanation:

Suppose you have a function f and its inversef −1 .

The points that the inverse function f −1 goes through can indeed be found by swapping the x-coordinates and y-coordinates of the original function f.

For a point (a,b) on the graph of f, it means that f(a)=b.

When we find the inverse function f −1 , it essentially undoes the operation of f.

So, if f −1 goes through the point (b,a), it means that f −1 (b)=a.

The points that the inverse function, f-1(x), goes through can be found by swapping the x-coordinates and y-coordinates of the original function, f(x).

So, if f(x) goes through the points (1,4) and (4,6), then f-1(x) will go through the points (4,1) and (6,4).