Find domain of the function root 4 - x square
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Answer:
The domain of any function is the set of values of
x
that can produce a real output
y
or
f
(
x
)
So you would bear with me that if
4
−
x
2
is negative then you have you would have the square root of a negative number which is imaginary and not real
Hence the function returns a real value when
4
−
x
2
is positive or zero
That is
4
−
x
2
≥
0
Hence we find the range of value that the above inequality represents,
Here we go,
4
−
x
2
≥
0
⇒
(
2
−
x
)
(
2
+
x
)
≥
0
⇒
−
1
⋅
(
x
−
2
)
(
x
+
2
)
≥
0
⇒
(
x
−
2
)
(
x
+
2
)
≤
0
Explanation:
−
2
≤
x
≤
2
is the required domain!
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