By using the table, we see that the correct options are:
a) f(2) = 7
b) f(x) = 3 when x = 8.
c) f⁻¹(7) = 2
d) f⁻¹(x) = 8 when x = 3.
How to use the information in the table?
Here we have a table of x and f(x).
First, we want to find f(2). To get that, we need to go to the row where we have x = 2.
In that same row we can see that f(x) = 7.
Then f(2) = 7.
Then it says:
"if f(x) = 3, then x = ?"
This time we do the opposite. We find the row where f(x) = 3, and then we see the value of x in that row.
In the second row (counting from the bottom) we can see that when x = 8, f(x) = 3.
Then:
"if f(x) = 3, x = 8"
Then we want to get the inverse of f(x) evaluated in 7.
Here we use the rule:
[tex]f(x) = y\\f^{-1}(y) = x[/tex]
Then
[tex]f(2) = 7\\f^{-1}(7) = 2[/tex]
The answer here is 2.
Finally:
"if the inverse evaluated in x si 8, then what is the value of x"
Similar to before, we know that when we evaluate f(x) in 8, the outcome is 3.
Then when we evaluate the inverse in 3, the outcome is 8.
So here we must have x = 3.
If you want to learn more about inverse functions:
https://brainly.com/question/14391067
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