Question

The inverse of the function f: R→R given by f(x) = 2x +7 is:

• A. 2(x+7)
• B. \(\frac{x+7}{2}\)
• C. x-7
• D. \(\frac{x-7}{2}\)

Answer 1

The Correct Option is D

The function given is \(f(x) = 2x + 7\). To find the inverse \(f^{-1}(x)\), follow these steps:

1. Replace \(f(x)\) with \(y\): \(y = 2x + 7\).
2. Swap \(x\) and \(y\) to find the inverse: \(x = 2y + 7\).
3. Solve for \(y\):

   • Subtract 7 from both sides:
     \(x - 7 = 2y\).
   • Divide both sides by 2:
     \(y = \frac{x - 7}{2}\).

The inverse function is \(f^{-1}(x) = \frac{x-7}{2}\), matching the correct answer.