For what values of x is the expression below undefined?

Question

x²-7+10

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x-4

Answer 1

The expression (X^2 -7x+10 ) / (x-4) is a rational expression and the domain of this expression is ALL real numbers for which the expression is definedl. Because the value of X=4 creates a value for which the expression is undefined because it gives an expression that equates to division by 0 and division by 0 is not defined, thus the expression is not defined at x = 4.

Answer 2

I'm going to assume you meant x²-7x+10

An expression becomes "undefined" when you plug in a number for x and the expression goes to infinity. This happens when the denominator is zero.

To visualize what this means, copy and paste this into google:

(x²-7x+10)/(x-4)

You can see on the graph that the line diverges at x=4. What that means is that one side of the line goes up as it gets closer to 4, and the other side goes down. So what is the value of the expression at x=4? at 3.999999...., the value is approaching infinity. However, at 4.00000...001, the value is approaching negative infinity from the opposite direction.

The value of the expression at 4 cannot be both infinity and negative infinity, so it's undefined.

You can tell where a statement is undefined by figuring out which value for x makes the denominator zero.