Question

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

Answer 1

Answer:

$c=-2$

Step-by-step 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.