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What is the inverse of the function f(x) = 3x - 5?

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Question: What is the inverse of the function f(x) = 3x - 5?

Options:

  1. (x + 5)/3
  2. (x - 5)/3
  3. 3(x + 5)
  4. 3(x - 5)

Correct Answer: (x + 5)/3

Solution: 

To find the inverse, set y = 3x - 5, solve for x: x = (y + 5)/3, hence f^(-1)(x) = (x + 5)/3.

What is the inverse of the function f(x) = 3x - 5?

Practice Questions

Q1
What is the inverse of the function f(x) = 3x - 5?
  1. (x + 5)/3
  2. (x - 5)/3
  3. 3(x + 5)
  4. 3(x - 5)

Questions & Step-by-Step Solutions

What is the inverse of the function f(x) = 3x - 5?
  • Step 1: Start with the function f(x) = 3x - 5.
  • Step 2: Replace f(x) with y, so now we have y = 3x - 5.
  • Step 3: To find the inverse, we need to solve for x in terms of y.
  • Step 4: Add 5 to both sides of the equation: y + 5 = 3x.
  • Step 5: Now, divide both sides by 3 to isolate x: x = (y + 5) / 3.
  • Step 6: The inverse function is written as f^(-1)(x). So, replace y with x: f^(-1)(x) = (x + 5) / 3.
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