Question

Consider the following system of equations. f(x) = x² + 9x - 3

g(x) = 9x – 84 .

Where is f(x) = g(x)? Select all that apply.

A)-9. B)-9i. C)-3. D)0. E)9. F)9i​

Answer 1

Only for the value of x = -9 i, f(x) = g(x)

Explanation:

Here,
`f(x) = x^(2)  + 9x -3 , g(x) = 9x -84`

Now, find the values of the given functions:

A) at x = -9

`f(x) = (-9)^(2)  + 9(-9) -3 = -3\\g(x) = 9(-9) - 84 = -165`

⇒ f(-9) ≠ g(-9)

B) at x = -9i

`f(x) = (-9i)^(2)  + 9(-9i) -3 = -84 - 81i\\g(x) = 9(-9i) - 84 = -81i -84`

⇒ f(-9i) = g(-9i)= -84 - 81i

C) at x = -3

`f(x) = (-3)^(2)  + 9(-3) -3  = -26\\g(x) = 9(-3) - 84 = -111`

⇒ f(-3) ≠ g(-3)

D) at x = 0

`f(x) = (0)^(2)  + 9(0) -3  = -3\\g(x) = 9(0) - 84 = -84`

⇒ f(0) ≠ g(0)

E) at x = 9

`f(x) = (9)^(2)  + 9(9) -3  = 179\\g(x) = 9(9) - 84 = -3`

⇒ f(9) ≠ g(9)

F) at x = 9i

`f(x) = (9i)^(2)  + 9(9i) -3 = -3\\g(x) = 9(9i) - 84 = 81i -84`

⇒ f(-9i) ≠ g(-9i)

Hence, only for x = -9i, f(x) = g(x)