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What is the domain of #(-3x^2)/(x^2+4x-45)#?

Answer 1

The domain is all the real #x# except:
#x=-9# and #x=5#

In this division you must ensure to avoid a division by zero, i.e., to have a zero in the denominator. The denominator is equal to zero when: #x^2+4x-45=0# This is a quadratic equation that you can solve, say, using the Quadratic Formula. So: #x_(1,2)=(-4+-sqrt(16+180))/2=(-4+-14)/2=# so you have two values of #x# that makes the denominator equal to zero: #x_1=(-4+14)/2=5# #x_2(-4-14)/2=-9# These two values cannot be used by your function. All the other values of #x# are allowed:

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Answer 2

Eva Abramson

The domain of the function (-3x^2)/(x^2+4x-45) is all real numbers except for values of x that make the denominator equal to zero. To find these values, you can factor the quadratic expression in the denominator and solve for x.

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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.