Answer:
Only for the value of x = -9 i, f(x) = g(x)
Step-by-step explanation:
Here, [tex]f(x) = x^{2} + 9x -3 , g(x) = 9x -84[/tex]
Now, find the values of the given functions:
A) at x = -9
[tex]f(x) = (-9)^{2} + 9(-9) -3 = -3\\g(x) = 9(-9) - 84 = -165[/tex]
⇒ f(-9) ≠ g(-9)
B) at x = -9i
[tex]f(x) = (-9i)^{2} + 9(-9i) -3 = -84 - 81i\\g(x) = 9(-9i) - 84 = -81i -84[/tex]
⇒ f(-9i) = g(-9i)= -84 - 81i
C) at x = -3
[tex]f(x) = (-3)^{2} + 9(-3) -3 = -26\\g(x) = 9(-3) - 84 = -111[/tex]
⇒ f(-3) ≠ g(-3)
D) at x = 0
[tex]f(x) = (0)^{2} + 9(0) -3 = -3\\g(x) = 9(0) - 84 = -84[/tex]
⇒ f(0) ≠ g(0)
E) at x = 9
[tex]f(x) = (9)^{2} + 9(9) -3 = 179\\g(x) = 9(9) - 84 = -3[/tex]
⇒ f(9) ≠ g(9)
F) at x = 9i
[tex]f(x) = (9i)^{2} + 9(9i) -3 = -3\\g(x) = 9(9i) - 84 = 81i -84[/tex]
⇒ f(-9i) ≠ g(-9i)
Hence, only for x = -9i, f(x) = g(x)
