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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