How do you find the domain of #f(x) = (sqrt[x - 5](x - 6))/(x^2 - 7x + 6)#?

1 Answer
Daniel L.
Apr 20, 2015

The answer is : #D = (5;6) uu (6;oo) #

The domain of a function is this subset of real numbers for which all the operations in the functions have sense.

In this case
1) the expression #x-5# must be greater than or equal to zero (the square roots of negative numbers are not real)
2) the expression in denominator #x^2-7x+6# cannot be zero (You cannot divide by zero).

From first condition you get an inequality #x-5 >=0 # which has a solution #x in (5; +oo)#

Second condition leads to solving a square equation #x^2-7x+6!=0#
For this equation #Delta = 7^2 - 4*1*6 = 25#
#sqrt(Delta) = 5#
#x_1=2; x_2=6#

So the answer is #D = (5;6) uu (6;oo) #

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