Question

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

I.f(2) when f(x) = 3x + 2
II.f-1(3) when f(x) = 2 x minus 7, all over 3
III.2y + 14 = 4y - 2

Answer 1

f(x) = 3x +2

f(2) = 3(2) + 2 = 8

Now

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

let f(x) = y and f(y) = x;

y = (2x -7) / 3

x = (3y + 7) / 2

So

f(y) = (3y + 7) / 2

this f(y) is the inverse of f(x); hence

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

Now f^-1(3) = (9+7) / 2 = 8

For the third and last part,

2y + 14 = 4y – 2

2y = 16

y = 8

Hence all the three parts gives the same results.