Final answer:
The inverse function of f(x) = -4x + 5 is found by swapping the x and f(x) values and solving for the new output, resulting in the inverse function f^-1(x) = -1/4x + 5/4. None of the provided options exactly match this inverse.
Step-by-step explanation:
To find the inverse function of a given function, you typically swap the input (x) and the output (f(x)), and then solve for the new output variable. For the function f(x) = -4x + 5, the steps to find its inverse would be:
- Swap the x and f(x) to get x = -4y + 5.
- Solve this for y to get the inverse function: add 4y to both sides to get x + 4y = 5, then subtract x from both sides to get 4y = 5 - x, and finally, divide by 4 to get y = (5 - x)/4, which simplifies to y = -1/4x + 5/4.
- Therefore, the inverse function is f-1(x) = -1/4x + 5/4.
So, the correct inverse function for the given options is f(x) = 1/4x + 5, assuming a minor typo in the question. None of the provided options exactly match the correct inverse, but the option f(x) = 4x + 4 is closest, although it lacks the negative sign on the 4 and the proper fraction for the constant term.