Answered

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Which equation is the inverse of [tex] y = 7x^2 - 10 [/tex]?

A. [tex] y = \frac{\pm \sqrt{x+10}}{7} [/tex]

B. [tex] y = \pm \sqrt{\frac{x+10}{7}} [/tex]

C. [tex] y = \pm \sqrt{\frac{x}{7} + 10} [/tex]

D. [tex] y = \frac{\pm \sqrt{x}}{7} \pm \frac{\sqrt{10}}{7} [/tex]

Sagot :

GinnyAnswer
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]
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