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What is the inverse of the function f(x) = 2x + 3?

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Question: What is the inverse of the function f(x) = 2x + 3?

Options:

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

Correct Answer: (x - 3)/2

Solution: 

To find the inverse, set y = 2x + 3, solve for x: x = (y - 3)/2.

What is the inverse of the function f(x) = 2x + 3?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the inverse of the function f(x) = 2x + 3?
Correct Answer: f^(-1)(x) = (x - 3)/2
  • Step 1: Start with the function f(x) = 2x + 3. We want to find its inverse.
  • Step 2: Replace f(x) with y. So, we write y = 2x + 3.
  • Step 3: To find the inverse, we need to solve for x in terms of y. Start by isolating the term with x.
  • Step 4: Subtract 3 from both sides: y - 3 = 2x.
  • Step 5: Now, divide both sides by 2 to solve for x: x = (y - 3) / 2.
  • Step 6: The inverse function is found by switching x and y. So, we write the inverse as f^(-1)(x) = (x - 3) / 2.
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