Question

Find the domain of the function (f/g)(x) given f (x)=x^2-4x-5 and g(x)=x^2-25

Answer 1

Answer:

all real numbers except ±5.

Step-by-step explanation:

Each function (f(x), g(x)) has a domain that is all real numbers. Their quotient (f(x)/g(x)) must exclude values that make g(x) = 0. The quotient is undefined when the denominator is zero. Those excluded values are x = ±5.

The domain of (f/g)(x) is all real numbers except ±5.

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Of course you recognize x^2 -25 = 0 has solutions x = ±√25 = ±5. You can get there two ways:

1. add 25 and take the square root: x^2=25; x=±√25.
2. factor the difference of squares and set the factors to zero: (x-5)(x+5)=0 has solutions x-5=0 and x+5=0, that is, x = ±5.