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The function h is defined below.x-9h(x)=2x - 5x- 24Find all values of x that are NOT in the domain of h.If there is more than one value, separate them with commas.x = 08x?

The function h is defined belowx9hx2x 5x 24Find all values of x that are NOT in the domain of hIf there is more than one value separate them with commasx 08x class=

Respuesta :

we have the function

[tex]h(x)=\frac{x-9}{x^2-5x-24}[/tex]

Remember that

The denominator cannot be equal to zero

so

Solve the quadratic equation

[tex]x^2-5x-24=(x+3)(x-8)[/tex]

substitute in the original function

[tex]h(x)=\frac{x-9}{(x+3)(x-8)}[/tex]

therefore

The domain of the given function is the interval

(-infinite,-3) U (-3,8) U (8, infinite)

The values that are not in the domain are

-3 and 8

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