Question

find the inverse of f(x) = mx + b for what value or values of m or b does this functions not have an inverse that is also a function

Answer 1

To find the inverse of the function f(x) = mx + b, you can use the formula (x-b)/m. The function does not have an inverse that is also a function when m = 0 or when m ≠ 0 and b = 0.

Step-by-step explanation:

The inverse of the function f(x) = mx + b is given by the formula: f-1(x) = (x-b)/m. To find the value or values of m and b for which the function does not have an inverse that is also a function, we need to consider two scenarios:

1. If m = 0, then the function is a horizontal line and does not pass the vertical line test, meaning it does not have an inverse that is also a function.
2. If m ≠ 0 and b = 0, then the function is a vertical line and does not pass the horizontal line test, meaning it does not have an inverse that is also a function.