Step-by-step explanation:
We can observe from the table that the value of independent variable and then the values of function on that variable are given.
So,
f(5) = 6
As the value of function at x=5 is 6
If f(x) = 4 then x = 7
The value of function is 4 only on x=7 so the answer is x = 7
When the inverse is taken, the inputs become output and the outputs become inputs
[tex]f^{-1}(6) = 5[/tex]
The value of inverse will be 5 because in original function 5 is input and 6 is output when this will be reversed for inverse, the output will be 5 for 6
Now,
Lastly
[tex]if\ f^{-1}(x) = 7,\ then \x = 4[/tex]
The reverse rule of input and output will be used. The reverse function will generate 7 at input 4.
