What is the domain of $f (x) = \frac{1}{x^{2} - 4 x}$ $f(x)= 1/(x^2-4x)$ ?

Question

What is the domain of $f (x) = \frac{1}{x^{2} - 4 x}$ $f(x)= 1/(x^2-4x)$ ?

1 Answer

Impact of this question

5790 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-15T14:08:24

All real numbers except $x = 0$ $x=0$ and $x = 4$ $x=4$

Explanation:

The domain of a function is simply the set of all $x$ $x$ -values that will output real $y$ $y$ -values. In this equation, not all $x$ $x$ -values will work as we cannot divide by $0$ $0$ . Thus, we need to find when the denominator will be $0$ $0$ .

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

$x \cdot (x - 4) = 0$ $x*(x-4)=0$

Using the Zero Property of Multiplication, if $x = 0$ $x=0$ or $x - 4 = 0$ $x-4=0$ , then $x^{2} - 4 x = 0$ $x^2-4x=0$ will be $0$ $0$ .

Thus, $x = 0$ $x=0$ and $x = 4$ $x=4$ should not be part of the domain as they would result in a non-existent $y$ $y$ -value.

This means the domain is all real numbers except $x = 0$ $x=0$ and $x = 4$ $x=4$ .

In set notation, this can be written as $x in RR " such that " x!=0 and x!=4$

Science

Math

Humanities

... and beyond

What is the domain of $f (x) = \frac{1}{x^{2} - 4 x}$ $f(x)= 1/(x^2-4x)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the domain of f(x)= 1/(x^2-4x)f(x)=1x2−4x f(x)= 1/(x^2-4x)?

1 Answer

Explanation:

Related questions

Impact of this question

What is the domain of $f (x) = \frac{1}{x^{2} - 4 x}$ $f(x)= 1/(x^2-4x)$ ?