If f(x)=x^2+5x+6 and g(x)=3x+1, what is the domain of f(x)/g(x)?

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`(f(x))/(g(x)) = (x^2+5x+6)/(3x+1)`

This function...

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tonys538 | Student

The domain of a function y = f(x) is all the values that x can take for which y = f(x) is real and defined.

For f(x)=x^2+5x+6 and g(x)=3x+1, the value of y = f(x)/g(x) = (x^2 + 5x +6)/(3x+1)

= (x^2 + 2x + 3x + 6)/(3x+1)

= (x(x + 2) + 3(x + 2))/(3x+1)

= ((x+3)(x+2))/(3x+1)

The value of the numerator is defined for all values of x, the expression (f(x))/(g(x)) is not defined if g(x) = 0

3x+1 = 0

x = -1/3

The domain of (f(x))/(g(x)) is the set of real values except x = -1/3

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