Question

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

Answer 1

Answer:

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

Step-by-step 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.