Question

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

I. f(1) when f(x) = 4x - 1
II. f^-1(2) when f(x) = 3x - 1 over 4
III. 2y + 8 = 4y - 2
a) I and II
b) I and III
c) II and III
d) All three have different results.

Answer 1

Option C). Statement II. f^-1(2) when f(x) = 3x - 1 over 4 has the same result as statement III. 2y + 8 = 4y - 2. Let's solve each statement step by step.

Step-by-step explanation:

The statement II. f^-1(2) when f(x) = 3x - 1 over 4 has the same result as statement III. 2y + 8 = 4y - 2.

Let's solve each statement step by step:

1. Statement I. f(1) when f(x) = 4x - 1:
   Plug in x=1 into the function f(x)
   f(1) = 4(1) - 1
   f(1) = 4 - 1
   f(1) = 3
2. Statement II. f^-1(2) when f(x) = 3x - 1 over 4:
   First, solve the equation f(x) = 2 for x:
   3x - 1 over 4 = 2
   3x - 1 = 2*4
   3x - 1 = 8
   3x = 9
   x = 3
3. Statement III. 2y + 8 = 4y - 2:
   First, solve the equation 2y + 8 = 4y - 2 for y:
   2y - 4y = -2 - 8
   -2y = -10
   y = 5

Therefore, statements II and III have the same result.