Respuesta :
keep in mind that, to get the inverse expression of any relation, we start off by doing a quick switcharoo on the variables, and then solve for "y", so let's do so,
[tex]\bf y=9x^2-4\qquad \stackrel{inverse}{\boxed{x}=9\boxed{y}^2-4}\implies x+4=9y^2 \\\\\\ \cfrac{x+4}{9}=y^2\implies \sqrt{\cfrac{x+4}{9}}=\stackrel{f^{-1}(x)}{y}[/tex]
[tex]\bf y=9x^2-4\qquad \stackrel{inverse}{\boxed{x}=9\boxed{y}^2-4}\implies x+4=9y^2 \\\\\\ \cfrac{x+4}{9}=y^2\implies \sqrt{\cfrac{x+4}{9}}=\stackrel{f^{-1}(x)}{y}[/tex]
The inverse of the given equation is gotten as;
f⁻¹(x) = ±√((x + 4)/9)
We are given the equation;
y = 9x² - 4
To find the inverse, we first have to make x the subject of the formula;
y = 9x² - 4
- Using addition property of equality, add 4 to both sides;
y + 4 = 9x² - 4 + 4
y + 4 = 9x²
- Using division property of equality, divide both sides by 9;
(y + 4)/9 = 9x²/9
(y + 4)/9 = x²
Taking square root of both sides gives;
±√((y + 4)/9) = x
The inverse will be gotten by replacing y with x. Thus, the inverse is;
f⁻¹(x) = ±√((x + 4)/9)
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