document.write( "Question 246026: find the domain of the function: f(x)=log(base 7)(2-(x+5/x-6)i need to show the work \n" ); document.write( "
Algebra.Com's Answer #179716 by jsmallt9(3758)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "There are two issues to address here:
\n" ); document.write( "Denominator. \n" ); document.write( "Let's find what x value makes the denominator zero: \n" ); document.write( "x - 6 = 0 \n" ); document.write( "Add 6 to both sides: \n" ); document.write( "x = 6 \n" ); document.write( "This is a value we cannot allow for x. It must be excluded from the domain. \n" ); document.write( "Argument of the logarithm. \n" ); document.write( "We want a positive argument: \n" ); document.write( " \n" ); document.write( "There are different ways to solve this. One way is to subtract the terms on the left. Of course we need common denominators first: \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "Subtract (Be careful when subtracting!) : \n" ); document.write( " \n" ); document.write( "This says we have a positive fraction. When do we get positive fractions? Answer: When the numerator and denominator are both positive or when they are both negative. This idea, which you probably knew well, can be expressed in the algebraic form: \n" ); document.write( "( \n" ); document.write( "(Look at this and see if you can understand how this says \"both positive or both negative\".) \n" ); document.write( "Now we solve this compound inequality. \n" ); document.write( "( \n" ); document.write( "In the first pair, in order for x to be greater than 17 and 6, it would have to be greater than 17. In the last pair, in order for x to be less than 17 and 6, it would have to be less than 6. So \n" ); document.write( "( \n" ); document.write( "simplifies to \n" ); document.write( " \n" ); document.write( "Since |