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 minus 4, all over 5. III y + 10 = 2y + 1

Answer 1

F(x) = 2x + 2.....find f(3)
f(3) = 2(3) + 2
f(3) = 6 + 2
f(3) = 8

f(x) = (3x - 4)/5....find f^-1(4)
y = (3x - 4)/5...swap the variables
x = (3y - 4)/5 ...solve for y
5x = 3y - 4
5x + 4 = 3y
(5x + 4)/3 = y
f^-1(x) = (5x + 4)/3.....for f(4)
f(4) = (5(4) + 4)/3
f(4) = (20 + 4)/3
f(4) = 24/3
f(4) = 8

y + 10 = 2y + 1
y - 2y = 1 - 10
-y = -9
y = 9

so 1 and 2 have the same result...8