Question

For the function f(x) = - 4, find f–1(a).

of-1(x) = (9x + 4)
of-(x) = 9x2 + 4
of-'(x) = (9 (x + 4)
of-'(x) = 9 (x2 + 4)

Answer 1

The student has asked to find the inverse of the function f(x) = -4. However, since this is a constant function, it does not have an inverse function because it does not pass the Horizontal Line Test and does not have an inverse that is a function.

Step-by-step explanation:

The student is asking to find the inverse f–1(a) of the constant function f(x) = -4. However, it is important to note that a constant function does not have an inverse function in the traditional sense, as it does not pass the Horizontal Line Test; therefore, its inverse is not a function.

For non-constant functions, to find the inverse f–1(x), you typically swap the roles of x and y and solve for y. For example, if f(x) = (9x + 4), to find the inverse f–1(x), we would set y = (9x + 4) and then solve for x in terms of y, giving us an inverse f–1(x) which might resemble x = (y - 4)/9 after rearranging. However, since f(x) = -4 does not have a variable part, this process would not provide a meaningful result.