Answer:
- f⁻¹( f⁻¹(13)) = 9
- f⁻¹(8) = -13
Explanation:
The inverse of a function f(x) denoted by f⁻¹(x) is a function that undoes the f(x) action
To understand this better, let us assume that there is a function f(x) such that f(5) = 25. Then f⁻¹(25) = 5 which was the input for the function f(x)
To generalize,
f⁻¹(f(x)) = x
Dealing with the two questions
f⁻¹( f⁻¹(13))
The evaluation happens from the innermost evaluation to the outermost evaluation
So first determine f⁻¹(13)
Since 13 is an output f⁻¹(13) will give the x value which produced 13. The corresponding x value = 5 from the tables
Now use this in the original expression
f⁻¹( f⁻¹(13)) = f⁻¹(5)
Look at the table and determine where 5 appears in the output. Look at the x value corresponding to that and that will be f⁻¹(5)
From the table we can see that 5 is an output when x = 9 so
f⁻¹(5) = f⁻¹( f⁻¹(13)) = 9
f⁻¹(8)
Relatively easier since this is a straightforward task of locating the value 8 in the f(x) row and seeing what the corresponding x value is
From the table we see that for an output of 8, the input x = -13
So f⁻¹(8) = -13