Question

Assume that the function f is a one-to-one function.

Answer 1

Answer:

Assuming that the function f is a one-to-one function;

If f(3)=4, then f^-1(4) = 3

If f^-1(-8) = -9, then f(-9) = -8

Step-by-step explanation:

A function in which every value in the domain corresponds to exactly one value in the range is said to be a one-to-one function and it passes both the vertical and the horizontal line tests.

If a point (a,b) belongs to a one-to-one function f, the the point (b,a) belongs to its inverse.

In the first case we had f(3)=4 implying that the point (3,4) belongs to f and thus the point (4,3) will belong to the inverse of f. Thus, f^-1(4) = 3

Similarly, if f^-1(-8) = -9 the point (-8,-9) belongs to the inverse of f. This implies that the point (-9,-8) will belong to f. Thus, f(-9) = -8