Question

Given the function f(x) = -2c+cx-x^2, and f^-1(5) = -1, find c

Answer 1

`c=-2`

Explanation:

We are given the function:

`f(x) = -2c + cx - x^2`

And that:

`\displaystyle f^(-1) (5) = -1`

And we want to determine the value of c.

Recall that by definition of inverse functions:

`\displaystyle \text{If } f(a) = b, \text{ then } f^(-1)(b) = a`

So, since f⁻¹(5) = -1, then f(-1) = 5.

Substitute:

`f(-1) = 5 = -2c + c(-1) - (-1)^2`

Simplify:

`5 = -2c - c - (1)`

Combine like terms:

`6 = -3c`

And divide. Hence:

`c = -2`

In conclusion, the value of c is -2.