Question

If f is a one-to-one function and f(2)=8, then f^-1 (8)=
a) 2
b) 4
c) 6
d) 8

Answer 1

For a one-to-one function, if f(2) = 8, then its inverse f^-1(8) = 2 since an inverse function maps the range back to its original element in the domain.

Step-by-step explanation:

If f is a one-to-one function and f(2) = 8, then f-1(8) = 2. This is because the definition of a one-to-one function (also known as an injective function) ensures that each element of the range is uniquely paired with exactly one element of the domain. Therefore, the inverse function f-1 will map each element of the range back to its original element in the domain.

When given that f(2) = 8, we are told that the function f maps the number 2 to the number 8. The inverse function does the opposite, mapping the number 8 back to the number 2. Thus, f-1(8) will yield the value of 2, which is the element from the domain that was originally mapped to 8. Therefore, the correct answer is (a) 2.