Question

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

I.f(3) when f(x) = 2x + 2
II.f-1(4) when f(x) = (3x-4)/5
III.y + 10 = 2y + 1

Answer 1

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

f-1=(3x-4)/5-1=(3x-4-5)/5=(3x-9)/5 => f-1(4)=[(3*4)-9]/5=3/5

y+10=2y+1 => y=9

Answer 2

I. ) f ( 3 ) = 36 + 2 = 8
II. ) f ( x ) = ( 3 x - 4 ) / 5
y = ( 3 x - 4 ) / 5
5 y = 3 x - 4
5 y + 4 = 3 x
x = ( 5 y + 4 ) / 3
f-1(x ) = ( 5 x + 4 ) /3
f-1(4) = ( 20 + 4 ) / 3 = 24/3 = 8
III. ) y + 10 = 2 y + 1
- y = - 9
y = 9
Answer: The same result have I. and II.