the ordered pairs are:
[tex](x, y) = (x, \sqrt{\frac{9}{x} - 5 })\\\\x \neq 0\\x \geq 9/5[/tex]
How to find the inverse of the relation?
Here we have the relation:
[tex]x^2*y + 5y = 9[/tex]
That can be rewritten to:
[tex]y *(x^2 + 5) = 9\\\\y = \frac{9}{x^2 + 5}[/tex]
If the inverse is y = g(x), then:
[tex]\frac{9}{g(x)^2 + 5} = x[/tex]
Solving that for g(x) we get:
[tex]\frac{9}{g(x)^2 + 5} = x\\\\9 = x*(g(x)^2 + 5)\\\\\sqrt{\frac{9}{x} - 5 } = g(x)[/tex]
Where x can't be zero, and the argument of the square root must be zero or larger.
Then the ordered pairs are:
[tex](x, y) = (x, \sqrt{\frac{9}{x} - 5 })\\\\x \neq 0\\x \geq 9/5[/tex]
If you want to learn more about inverses:
https://brainly.com/question/14391067
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