Answer:
33. [tex]f^{-1}(7) = 6[/tex]
34. [tex]f^{-1}(2) = 3[/tex]
35. [tex]f(-8) = -4[/tex]
36. [tex]f(-1) = -2[/tex]
37. [tex]f(1) = 0[/tex]
38. [tex]x = 7[/tex]
39. [tex]f^{-1}(0) = 1[/tex]
40. [tex]f^{-1}(3) = 7[/tex]
Step-by-step explanation:
The inverse function [tex]f^{-1}(x)[/tex] points back from f(x) to x, that is, if we have [tex]f(x) = y[/tex], then we have that [tex]f^{-1}(y) = x[/tex], and if we have [tex]f^{-1}(y) = x[/tex], then we have [tex]f(x) = y[/tex]
So we have that:
33.
[tex]f(6) = 7[/tex]
[tex]f^{-1}(7) = 6[/tex]
34.
[tex]f(3) = 2[/tex]
[tex]f^{-1}(2) = 3[/tex]
35.
[tex]f^{-1}(-4) = -8[/tex]
[tex]f(-8) = -4[/tex]
36.
[tex]f^{-1}(-2) = -1[/tex]
[tex]f(-1) = -2[/tex]
In the exercises from 37 to 40, we do the same above, but now using the values in the table given. So we have:
37.
if [tex]x = 1[/tex], [tex]f(1) = 0[/tex]
38.
if [tex]f(x) = 3[/tex], [tex]x = 7[/tex]
39.
We just need to find where f(x) = 0. If [tex]f(1) = 0[/tex], [tex]f^{-1}(0) = 1[/tex]
40.
We just need to find the value of f(7). If [tex]f(7) = 3[/tex], [tex]f^{-1}(3) = 7[/tex]
