Respuesta :

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In this case, we know [tex]g(x) = x + 3[/tex], and we are trying to find [tex]g^{-1}(7)[/tex].


So, we will need to find [tex]g^{-1}(x)[/tex]. Let's do that now:

[tex]y = x + 3[/tex]

  • Replace [tex]g(x)[/tex] with [tex]y[/tex]. This is just simple substitution, nothing major has happened yet.

[tex]x = y + 3[/tex]

  • Switch [tex]x[/tex] and [tex]y[/tex]. This is simply part of the process of finding the inverse function

[tex]y = x - 3[/tex]

  • Solve for [tex]y[/tex]

[tex]g^{-1}(x) = x - 3[/tex]

  • Replace [tex]y[/tex] with the notation for the inverse function

Now, we are going to solve for when [tex]x = 7[/tex]. To do this, simply "plug in" 7 for [tex]x[/tex] in the inverse function.

[tex]g^{-1}(7) = 7 - 3 = \boxed{4}[/tex]


Our answer is 4.

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