Final answer:
To find the inverse of the function f(x) = 1/2 x - 5, we switch x and y and solve for y to get the inverse function f¹(x) = 2x + 10.
Step-by-step explanation:
The student's question seems to be asking for the inverse function of f(x) = 1/2 x - 5. To find the inverse function, denoted f¹(x), we would first replace f(x) with y to get the equation y = 1/2 x - 5. Then we switch x and y, leading to x = 1/2 y - 5. Solving this equation for y gives us the inverse function. By multiplying both sides by 2 to eliminate the fraction, we get 2x = y - 10. After adding 10 to both sides, we have y = 2x + 10. Therefore, the inverse function is f¹(x) = 2x + 10.
We must ensure the function is one-to-one to have an inverse function. In this case, the original function is a linear function which is naturally one-to-one, ensuring the existence of its inverse.