SOLUTION: Given g(x) = 1/(4(x-5)^2 -1). For what value of x is function g undefined? My attempt: I take this to mean "for what value of x does the denominator = 0." Assuming that's correc

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Question 1006597: Given g(x) = 1/(4(x-5)^2 -1). For what value of x is function g undefined?
My attempt: I take this to mean "for what value of x does the denominator = 0." Assuming that's correct, I set the denominator equal to 0. I get a quadratic equation. I plug the coefficients into the quadratic formula, but I do NOT get the correct answer, which is supposed to equal 4 and 1/2.
I think I'm not doing the order of operations right in converting the denominator into the quadratic formula.
I won't belabor you with all my different attempts. Could someone show me how the math should go? The other answer choices are 5 and 1/4, 5, and 1. I did get to 5 and 1/4, but I do think that's wrong mathematically.
Thank you.

Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
There's no need to use the quadratic formula since that would require us to expand/simplify the left side. It's more work than needed in my opinion.


Since it's in vertex form, we can isolate x to get





Add 1 to both sides





Multiply both sides by 1/4





Apply the square root to both sides


Use the rule where x is any real number


or Split up the absolute value into the plus/minus components


or For each equation, add 5 to both sides


or


or


-------------------------------------------


So the two solutions to are...


or

------------------------------------------


So g(x) is undefined when or

Side Notes:


Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Look for the zeros of the denominator, the values of x which make the denominator 0. This you
can do easily because the denominator is a quadratic expression in standard form.

The solution to will be the values of x for which the function g(x) is undefined.







and are the values which are UNDEFINED for x in g.

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