To find the inverse of the function \( y = 7x^2 - 10 \), follow these steps:
1. Swap \( x \) and \( y \):
[tex]\[ x = 7y^2 - 10 \][/tex]
2. Solve for \( y \):
- Add 10 to both sides of the equation:
[tex]\[ x + 10 = 7y^2 \][/tex]
- Divide both sides by 7:
[tex]\[ \frac{x + 10}{7} = y^2 \][/tex]
- Take the square root of both sides:
[tex]\[ y = \pm \sqrt{\frac{x + 10}{7}} \][/tex]
Therefore, the equation of the inverse function is:
[tex]\[ y = \pm \sqrt{\frac{x + 10}{7}} \][/tex]
So, the correct answer is:
[tex]\[ y = \pm \sqrt{\frac{x + 10}{7}} \][/tex]
