Question

= x {}^{2} + 12x + 36" alt="f(x) = x {}^{2} + 12x + 36" align="absmiddle" class="latex-formula">
Determine the value of f^-1 (225) in this situation.
A. 21 days

B. 9 days

C. 6 days

D. 15 days​

Answer 1

Answer:

B

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = x^2 + 12x + 36$

And we want to determine the value of:

$\displaystyle f^{-1}(225)$

Let this value equal a. In other words:  

$\displaystyle f^{-1}(225) = a$

Then by the definition of inverse functions:

$\displaystyle \text{If } f^{-1}(225) = a\text{, then } f(a) = 225$

Hence:

$\displaystyle f(a) =225 = (a)^2 + 12(a) + 36$

Solve for a:

$\displaystyle \begin{aligned} 225 &= a^2 + 12a + 36 \\ \\ a^2 + 12a -189 &= 0 \\ \\ (a + 21)(a-9) &= 0\end{aligned}$

By the Zero Product Property:

$\displaystyle a + 21 = 0 \text{ or } a - 9 = 0$

Hence:

$\displaystyle a = -21 \text{ or } a = 9$

Thus, f(9) = 225. Consequently, f⁻¹(225) = 9.

In conclusion, our answer is B.