Assume that the function f is a one-to-one function, (a) f(8) = 9, find f ^ -1 (9) also if f ^ -1 (-7) = -3, find f (-3)

We want to find some values of the inverse of a function, knowing that the function is one-to-one.

The solutions are:

a) f⁻¹(9) = 8.

b) f(-3) = -7

A one-to-one function is a function that assigns each point in the domain to a unique point in the range (such that each point on the range is mapped from only one point on the domain).

If a function is one-to-one, then it can have an inverse function, such that if f(x) is our function and f⁻¹(x) is the inverse function, we have that:

f(f⁻¹(x)) = x = f⁻¹(f(x))

a) f(8) = 9

We want to find:

f⁻¹(9)

We can write:

f⁻¹( f(8) = 9) = 8

f⁻¹(9) = 8.

b) f⁻¹(-7) = -3

Now we want to find:

f(-3)

Then we can write:

f( f⁻¹(-7) = -3) = f( f⁻¹(-7)) = -7

f(-3) = -7

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(a) since we are given that f(8) = 9, the inverse of 9 is simply 8. Therefore, f^-1(9) = 8.

(b) Again, f is the inverse of f^-1, therefore, you simply switch numbers, and you get that f(-3) = -7.

3 is greater then both of those numbers