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How do you find the domain for #f(x) = (4x^2 - 9)/(x^2 + 5x + 6)#?

Answer 1

To find the domain, we only need to factor the denominator to find its zeros. Other than the denominator being zero, #f(x)# is well defined for all #x in RR#.

#x^2+5x+6 = (x+3)(x+2)#

which is zero when #x = -3# or #x=-2#

So the domain of #f(x)# is:

#(-oo, -3) uu (-3, -2) uu (-2, oo)#

That is #{x in RR : x != -3 and x != -2}#

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Answer 2

Isaiah Anthony

To find the domain of the function f(x) = (4x^2 - 9)/(x^2 + 5x + 6), we need to determine the values of x for which the function is defined.

The function is defined for all real numbers except the values that make the denominator equal to zero.

To find these values, we set the denominator equal to zero and solve for x:

x^2 + 5x + 6 = 0

Factoring the quadratic equation, we have:

(x + 2)(x + 3) = 0

Setting each factor equal to zero, we get:

x + 2 = 0 or x + 3 = 0

Solving these equations, we find:

x = -2 or x = -3

Therefore, the domain of the function f(x) is all real numbers except x = -2 and x = -3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.