Question

Which statement explains why the solution to the equation is x=4

Answer 1

C. The
`x`-value of 4 produces the same
`y`-value in both
`f(x) = (x-2)^(3)-6` and
`g(x) = \sqrt[3]{x+4}`.

Explanation:

Let
`f(x) = (x-2)^(3)-6` and
`g(x) = \sqrt[3]{x+4}`. A value of
`x` is a solution of the formula if and only if
`f(x) = g(x)`. If we know that
`x = 4`, then values of each function are, respectively:

`f(x) = (x-2)^(3)-6`

`f(4) = 2^(3)-6`

`f(4) = 2`

`g(x) = \sqrt[3]{x+4}`

`g(4) = \sqrt[3]{8}`

`g(4) = 2`

Since
`f(4) = g(4)`, then
`x = 4` is a solution of
`(x-2)^(3)-6 = \sqrt[3]{x+4}`. Hence, correct answer is C.