Question

Show all workPLEASE HELP! !!!

Answer 1

(a) Using the table, give the values fo rthe inverse

1) original table of values:

x      1     2     3    4    5

f(x)   0     1     1    5    3


2) The inverse of the function is obtained by exchanging x and f(x), this is:

                   ( x, f(x) ) → ( f(x), x)

3) So, the table of values of the inverse of the given function is:

x          0    1     1      5     3

f⁻¹ (x)   0     1     2     3     4

(b) Is the inverse a function.

No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.

This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.