Respuesta :

Answer:

[tex]g(1) = \boxed{1}[/tex]

Step-by-step explanation:

The given function g(x), is a piecewise function which has different definitions for different x intervals

We are asked to find the value of g at x = 1 i.e. g(1)

Note that when x is not equal to either -2 or -1, the function definition is
[tex]g(x) = x^3 - x^2 + 1[/tex]

Since [tex]x = 1[/tex]  follows the property [tex]x \ne -2, -1[/tex]  the correct definition to use is
[tex]g(x) = x^3 - x^2 + 1[/tex]

Therefore
[tex]g(1) = 1^3 - 1^2 + 1\\\\[/tex]
[tex]g(1) = 1 - 1 + 1\\\\[/tex]
[tex]g(1) = \boxed{1}[/tex]

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