Respuesta :

ivycoveredwalls
We need to know the definition of the "combined function" h(x).  I'm going to guess--by looking at answers--that the function is [tex]h(x)=\frac{f(x)}{g(x)}[/tex] making it

[tex]h(x)=\frac{5x+1}{x^2-9}[/tex]

This function is undefined wherever the denominator is equal to 0 (division by zero is undefined).  Factor the denominator.

[tex]h(x)=\frac{5x+1}{(x+3)(x-3)}[/tex]

The two values of x that make the denominator 0 are 3 and -3, otherwise written [tex]x=\pm 3[/tex].
abidemiokin

The values of x for which the combined function h(x) is undefined if f(x) = 5x + 1 and g(x) = x² - 9 is ±3: Option C is correct.

Given the following functions;

f(x) = 5x + 1

g(x) = x² - 9

The combined function h(x) is expressed as [tex]h(x)=\frac{f(x)}{g(x)}[/tex]

Substitute the given functions into the combined function as shown:

[tex]h(x)=\frac{5x+1}{x^2-9}\\h(x)=\frac{5x+1}{x^2-3^2}\\h(x)=\frac{5x+1}{(x+3)(x-3)}[/tex]

For the function to be undefined, the denominator will be equated to zero

(x + 3)(x - 3) = 0

x + 3 = 0 and x - 3 = 0

x = 3 and -3

Hence the values of x for which the combined function h(x) is undefined if f(x) = 5x + 1 and g(x) = x² - 9 is ±3

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