Question

If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection? (0, –2) (1, –1) (2, 0) (3, 3)

Answer 1

Given info : If f(x) and its inverse function, f⁻¹(x) are both plotted on the same co-ordinate plane.

To find : what is their point of intersection ?

1. (0, –2)
2. (1, –1)
3. (2, 0)
4. (3, 3)

solution : if we draw the graph of a function , y = f(x) and its inverse, y = f⁻¹(x), we will see, inverse f⁻¹(x) is the mirror image of the given function with respect to y = x. it means, both can intersect each other only on y = x as you can see in figure.

    now we understand how they intersect each other, let's find the possible intersecting point.

∵ the intersecting point must lie on the line y = x.

now see which point satisfies the line y = x.

definitely, (3,3) is the only point which satisfies the line y =x.

therefore the point of intersection of function and its inverse would be (3,3).