Which of the following statements have the same result? Explain each step in solving each one.

f (2) when f (x) = 3x + 2

f-1 (3) when f (x) = 2 x minus 7, all over 3

2y + 14 = 4y - 2

1) f (x) = 3x + 2 = > f (2) = 3 (2) + 2 = 6 + 2 = 8

2) f (x) = [ 2x - 7] / 3

To find the inverse of the function f (x), call y = f (x), and exchange y and x

y = [2x - 7] / 3

x = [2y - 7] / 3 = > 2y - 7 = 3x = > y = [3x + 7] / 2

y = f^-1 (x) = [3x + 7] / 2

f^-1 (3) = [3 (3) + 7 ] / 2 = (9+7) / 2 = 16 / 2 = 8

3) 2y + 14 = 4y - 2

4y - 2y = 14 + 2

2y = 16 = > y = 16/2 = 8

Answer: the three statements have the same result