To find [tex]\( g(4z) \)[/tex] where the function [tex]\( g \)[/tex] is defined as [tex]\( g(x) = 2x^2 - 7 \)[/tex]:
1. First, identify the original function [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = 2x^2 - 7
\][/tex]
2. Substitute [tex]\( 4z \)[/tex] in place of [tex]\( x \)[/tex] in the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(4z) = 2(4z)^2 - 7
\][/tex]
3. Calculate [tex]\( (4z)^2 \)[/tex]:
[tex]\[
(4z)^2 = 16z^2
\][/tex]
4. Substitute [tex]\( 16z^2 \)[/tex] back into the function:
[tex]\[
g(4z) = 2 \cdot 16z^2 - 7
\][/tex]
5. Simplify the expression:
[tex]\[
2 \cdot 16z^2 = 32z^2
\][/tex]
So,
[tex]\[
g(4z) = 32z^2 - 7
\][/tex]
Thus, the result is:
[tex]\[
g(4z) = 32z^2 - 7
\][/tex]
