Consider the equation below.
(I - 2)² – 6 = 8 + 4
Which statement explains why the solution to the equation is r = 4?
A
6 and
gir) =
T + 4.
B.
-
6 and
The x-va
lue of 4 is defined on the graphs of both flom) = (x - 2)
The x-value of 4 is a x-intercept for both f(x) = (1 – 2)8
gir) =
3 + 4
OC. The x-value of 4 is undefined for both f(x)
(x - 2)
g(3)
D. The x-value of 4 produces the same y-value in both f(x)
(x - 2) 6 and
gir)
-
6 and
(x + 4.
or + 4.

Answer:

answer is B

Step-by-step explanation:

The solution to the equation is 4 or x = 4 because the x-value of 4 produces the same y-value in both f(x) = (x - 2)³ – 6 and g(x) = ∛(x + 4) option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have an equation in terms of x:

(x - 2)³ – 6 = ∛(x + 4)

To find the value of x we can solve it by trial and error method:

Plug x = 4 in the equation:

(4 - 2)³ – 6 = ∛(4 + 4)

(2)³ – 6 = ∛(8)

8 - 6 = 2

2 = 2 (true)

The solution to the equation is x = 4

Thus, the solution to the equation is 4 or x = 4 because the x-value of 4 produces the same y-value in both f(x) = (x - 2)³ – 6 and g(x) = ∛(x + 4) option (D) is correct.

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