To determine the inverse of the function [tex]\( y = 7x^2 - 10 \)[/tex], we follow these steps:
1. Start with the original function:
[tex]\[
y = 7x^2 - 10
\][/tex]
2. Swap the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to begin solving for the inverse:
[tex]\[
x = 7y^2 - 10
\][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
x = 7y^2 - 10
\][/tex]
Add 10 to both sides:
[tex]\[
x + 10 = 7y^2
\][/tex]
Divide both sides by 7:
[tex]\[
\frac{x + 10}{7} = y^2
\][/tex]
4. Take the square root of both sides to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \pm \sqrt{\frac{x + 10}{7}}
\][/tex]
Thus, the inverse function of [tex]\( y = 7x^2 - 10 \)[/tex] is given by:
[tex]\[
y = \pm \sqrt{\frac{x + 10}{7}}
\][/tex]
Therefore, the correct answer is:
[tex]\[
y = \pm \sqrt{\frac{x + 10}{7}}
\][/tex]
