Certainly! Let's break down the problem step-by-step to find the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex] in the equation [tex]\( g(x) = \sqrt[3]{x-n} + k \)[/tex].
Given equation:
[tex]\[
g(x) = \sqrt[3]{x-n} + k
\][/tex]
We are given the values:
[tex]\[
h = 2
\][/tex]
[tex]\[
k = -2
\][/tex]
By substituting these values into the equation, we can identify [tex]\( h \)[/tex] was incorrectly mentioned and actually find the corresponding variable that matches these values.
First, substitute the given values:
[tex]\[
h = 2
\][/tex]
[tex]\(
g(x) = \sqrt[3]{x - h} + k = \sqrt[3]{x - 2} - 2
\)[/tex]
Given results honest values mean:
[tex]\[
g(x) = \sqrt[3]{x - n} + k = \sqrt[3]{x - 2} - 2
\][/tex]
Reading the correct terms:
[tex]\[
h = 2
\][/tex]
[tex]\(
k = -2
\)[/tex]
So, the solution can be summarized as:
[tex]\[
h = 2
\][/tex]
[tex]\(
k = -2
\]
Thus, the function rule incorporates these values and defines:
\(
g(x) = \sqrt[3]{x - 2} - 2
\)[/tex]
Hence,
[tex]\[
h = 2 \quad \text{and} \quad k = -2.
\][/tex]
