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If f(x) = 3x - 4, what is the inverse function f^(-1)(x)?

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Question: If f(x) = 3x - 4, what is the inverse function f^(-1)(x)?

Options:

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

Correct Answer: (x + 4)/3

Solution: 

To find the inverse, set y = 3x - 4, solve for x: x = (y + 4)/3, thus f^(-1)(x) = (x + 4)/3.

If f(x) = 3x - 4, what is the inverse function f^(-1)(x)?

Practice Questions

Q1
If f(x) = 3x - 4, what is the inverse function f^(-1)(x)?
  1. (x + 4)/3
  2. 3x + 4
  3. 3(x - 4)
  4. x/3 + 4

Questions & Step-by-Step Solutions

If f(x) = 3x - 4, what is the inverse function f^(-1)(x)?
  • Step 1: Start with the function f(x) = 3x - 4.
  • Step 2: Replace f(x) with y, so we have y = 3x - 4.
  • Step 3: To find the inverse, we need to solve for x in terms of y.
  • Step 4: Add 4 to both sides of the equation: y + 4 = 3x.
  • Step 5: Now, divide both sides by 3 to isolate x: x = (y + 4) / 3.
  • Step 6: The inverse function is written as f^(-1)(x), so replace y with x: f^(-1)(x) = (x + 4) / 3.
  • Inverse Functions – Understanding how to find the inverse of a function by swapping x and y and solving for y.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables.
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