Question

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

Answer 1

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