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What is the inverse of the function f(x) = 2x + 5?

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Question: What is the inverse of the function f(x) = 2x + 5?

Options:

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

Correct Answer: f^-1(x) = (x - 5)/2

Solution: 

To find the inverse, set y = 2x + 5, solve for x: x = (y - 5)/2, thus f^-1(x) = (x - 5)/2.

What is the inverse of the function f(x) = 2x + 5?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the inverse of the function f(x) = 2x + 5?
  • Step 1: Start with the function f(x) = 2x + 5.
  • Step 2: Replace f(x) with y, so now we have y = 2x + 5.
  • Step 3: We want to solve for x in terms of y. First, subtract 5 from both sides: y - 5 = 2x.
  • Step 4: Now, divide both sides by 2 to isolate x: x = (y - 5) / 2.
  • Step 5: The inverse function is found by replacing y with x: f^-1(x) = (x - 5) / 2.
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