High School

What is the inverse of the function \( f(c) = 95c + 32 \)?

A. \( f^{-1}(c) = \frac{c - 32}{95} \)
B. \( f^{-1}(c) = \frac{c + 32}{95} \)
C. \( f^{-1}(c) = (c - 32) \times 95 \)
D. \( f^{-1}(c) = (c + 32) \times 95 \)

Answer :

Final answer:

To find the inverse of the function f(c) = 95c + 32, we swap the variables and solve for the new dependent variable, which yields the inverse function f^(-1)(c) = (c - 32)/95. So the option number C is correct.

Explanation:

The question asks for the inverse of the function f(c) = 95c + 32. To find the inverse of a function, we swap the dependent and independent variables and solve for the new dependent variable. Let's go through the steps:

  1. Start with the original function: f(c) = 95c + 32.
  2. Replace f(c) with y: y = 95c + 32.
  3. Swap y and c: c = 95y + 32.
  4. Solve for y: y = (c - 32) / 95.

Therefore, the inverse function is f^(-1)(c) = (c - 32)/95, which corresponds to option a.

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