Find the domain in $y = \sqrt{4 - x}$ $y=sqrt(4-x)$ ?

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Find the domain in $y = \sqrt{4 - x}$ $y=sqrt(4-x)$ ?

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Answer 1 · 2018-03-19T01:59:03

$x \leq 4$ $x<=4$ or $(- \infty, 4]$ $(-oo,4]$

Explanation:

Since this is a square root, the values inside cannot be lesser that 0. Else, you would end up with an imaginary number. So, with that information, we can write the inequality:

$4 - x \geq 0$ $4-x>=0$

Solve for $x$ $x$ :

$\Rightarrow - x \geq 0 - 4$ $=> -x>=0-4$

$\Rightarrow - x \geq - 4$ $=>-x>=-4$

Now, when we multiply both sides by a negative, we have to switch the signs:

$(- 1) - x \leq (- 1) - 4$ $(-1)-x<=(-1)-4$

$x \leq 4$ $x<=4$

We can also represent this as:

$(- \infty, 4]$ $(-oo,4]$

And there we have our answer.

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