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 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]
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