What is the domain of  f(x) = (x+1)/(x^2 - 7x + 12)

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taylormath's profile pic

taylormath | High School Teacher | (Level 2) Adjunct Educator

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The domain of a function represents all the input, usually x-values that can safely be substituted into the function.  One of the main rules that must be obeyed is to never divide by zero.  In the function, f(x)=(x+1)/(x^2-7x+12), the denominator should never equal zero.  To find the x-values that the domain cannot equal, set x^2-7x+12=0 and solve.

x^2-7x+12=0

(x-4)(x-3)=0

x=4 or x=3

The domain, x, is all real numbers except x can not equal 4 or 3.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find the domain of f(x) = (x+1)/(x^2 - 7x + 12)

The domain is the set of all values of the independent variable x for which f(x) is defined.

f(x) = (x+1)/(x^2 - 7x + 12) is defined for all values of x except those that make x^2 - 7x + 12 = 0. When the denominator is 0, we get a number of the form (x - 1)/0 which is indeterminate.

x^2 - 7x + 12 = 0

=> x^2 – 4x – 3x + 12 = 0

=> x(x – 4) – 3(x – 4) = 0

=> (x – 4)(x – 3) = 0

The denominator becomes 0 when x = 4 and when x = 3

The domain of the function is R – {3, 4}

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