Question

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

f(1) when f(x) = 5x + 1
f-1(3) when f(x) = "2x plus 3, all over 5
3y - 7 = y + 5

Answer 1

1 )
f ( 1 ) = 5 * 1 + 1 = 5 + 1 = 6
2 )
f ( x ) = (2 x + 3) / 5 ( we have to find an inverse function )
y = ( 2 x + 3 ) / 5
5 y = 2 x + 3
2 x = 5 y - 3
x = ( 5 y - 3 ) / 2
f^(-1) ( x ) = ( 5 x - 3 ) / 2
f^(-1) ( 3 ) = ( 15 - 3 ) / 2 = 12 / 2 = 6
3 )
3 y - 7 = y + 5
3 y - y = 5 + 7
2 y = 12
y = 6
Answer: All have the same result.