SOLUTION: Given that a,b, and c are constants, a<b<c, state the domain y= sqrt((x-a)(x-b)(x-c)) Hint: Graph y=(x-a)(x-b)(x-c)

Question 1133768: Given that a,b, and c are constants, a y= sqrt((x-a)(x-b)(x-c))
Hint: Graph y=(x-a)(x-b)(x-c)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For the square root of an expression to be a real number, the expression has to be zero or positive.

In this example, the expression under the radical is (x-a)(x-b)(x-c), and we are given the condition that a < b < c.

That expression has the value 0 when x is a, b, or c; so the values a, b, and c are all in the domain.

For the intervals into which the rest of the number line is divided by those three values...

if x > c, then all three factors in the expression are positive, so the product is positive;
if b < x < c, then the factor (x-c) is negative, so the product is negative;
if a < x < b, then the factors (x-b) and (x-c) are both negative, so the product is positive; and
if x < a, then all three factors are negative, so the product is negative.

Now you should be able to determine the domain....
RELATED QUESTIONS
Given that f(x) = 2x^2 + x - 3,write f(x) in the form a(x+b)^2 + c,where a,b and c are... (answered by Edwin McCravy,mccravyedwin)

Given that f(x) = 2x^2 + x - 3,write f(x) in the form a(x+b)^2 + c,where a,b and c are... (answered by ikleyn)

. x + 3y − z = a x + y + 2z = b 2y − 3z = c solve the following systems,... (answered by josgarithmetic)

In the following equation a, b, and c are positive real numbers and a < b < c .... (answered by math_tutor2020)

Convert each of these linear equations into the form Y = mX + c,where a and b are... (answered by Edwin McCravy,ikleyn)

Suppose that A, B, and C are positive constants and that x+y= C. Show that the minimum... (answered by Edwin McCravy)

Convert these linear equations into the form Y= mX + c,where a and b are constants 1)... (answered by josgarithmetic)

Solve the inequality for x, assuming that a,b,and c are positive constants. a < or =... (answered by Boreal)

Solve for x; a, b & c are constants. 9x-b=c (answered by kateskute)