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Which equation is the inverse of y = x2 – 36?
y = plus-or-minus StartRoot x EndRoot + 6
y = plus-or-minus StartRoot x + 36 EndRoot
y = plus-or-minus StartRoot x EndRoot + 36
y = plus-or-minus StartRoot x squared + 36 EndRoot

Sagot :

Jacob193idn

Answer:

[tex]\displaystyle y = \pm \sqrt{x + 36}[/tex].

Step-by-step explanation:

To find the inverse of a function, apply the following steps:

  • Interchange [tex]x[/tex] and [tex]y[/tex].
  • Solve for [tex]y[/tex] in terms of [tex]x[/tex].

For the equation in this question, interchanging [tex]x[/tex] and [tex]y[/tex] yields [tex]x = y^{2} - 36[/tex]. Simplify and solve this equation for [tex]y[/tex]:

[tex]y^{2} = x + 36[/tex].

Before taking the square root of both sides, note that both [tex](-1)^{2}[/tex] and [tex]1^{2}[/tex] are equal to [tex]1[/tex]. In other words, both of the following would evaluate to [tex]x + 36[/tex]:

  • [tex]\sqrt{x + 36}[/tex].
  • [tex](-1)\, \sqrt{x + 36}[/tex].

Both [tex]y = \sqrt{x + 36}[/tex] and [tex]y = -\sqrt{x + 36}[/tex] are valid inverses of this function. To represent both in one equation:

[tex]\displaystyle y = \pm \sqrt{x + 36}[/tex].

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