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# x2+y-4=0 solve for x in getting the range of a function

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x2+y-4=0 solve for x in getting the range of a function

Aug 19, 2015

#2
+17747
+5

x2 + y - 4  =  0

If you want to solve for x:

Get the x-term alone on one side:

x2  =  4 - y

Then find the square root of both sides; remember that there are two answers:

x  =  √(4 - y)     or     x  =  -√(4 - y)

However, you don't need to do this to find the range ...

Solving for y:  y  =  x2 + 4

For any value of x, y must be at least 4 and can be any number greater than 4, so the range consists of  y  ≥  4.

Aug 19, 2015

#1
+5

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{4}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{y}}}}\\ {\mathtt{x}} = {\sqrt{{\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{y}}}}\\ \end{array} \right\}$$

.
Aug 19, 2015
#2
+17747
+5

x2 + y - 4  =  0

If you want to solve for x:

Get the x-term alone on one side:

x2  =  4 - y

Then find the square root of both sides; remember that there are two answers:

x  =  √(4 - y)     or     x  =  -√(4 - y)

However, you don't need to do this to find the range ...

Solving for y:  y  =  x2 + 4

For any value of x, y must be at least 4 and can be any number greater than 4, so the range consists of  y  ≥  4.

geno3141 Aug 19, 2015