Find Where Undefined/Discontinuous f(x)=(x^4-4x^2)/(x^2-4x)

$f (x) = \frac{x^{4} - 4 x^{2}}{x^{2} - 4 x}$

Set the denominator in $\frac{x^{4} - 4 x^{2}}{x^{2} - 4 x}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 4 x = 0$

Solve for $x$ .

Factor $x$ out of $x^{2} - 4 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x - 4 x = 0$

Factor $x$ out of $- 4 x$ .

$x \cdot x + x \cdot - 4 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 4$ .

$x (x - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $x (x - 4) = 0$ true.

$x = 0, 4$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = 0, x = 4$

Find Where Undefined/Discontinuous f(x)=(x^4-4x^2)/(x^2-4x)

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