Answer
The domain of the given function
f
(
x
) is the set of input values for which f
(
x
) is real and defined.
Point to note:
[tex]\sqrt f{x} = f x\geq 0[/tex]
Solve for (
x
−
1
) ≥
0 to obtain x ≥
1
.
Hence,
Domain: [tex]{x} \geq 1[/tex]
Interval Notation: [tex]1,[/tex]∞
Step 2:
Range:
Range is the set of values of the dependent variable used in the function f
(
x
) for which f(
x
) is defined.
Hence,
Range: f(
x) ≥
0
Range: f
(
x
) ≥
0
Interval Notation: [
0
,
∞
)
Step3:
Additional note:
The function y
=
f
(
x
)
=
√
x−
1 has no asymptotes.
Create a data table using values for x and corresponding values for y
:
Observe that Z
e
r
o and Negative values of x make the function f
(
x
)
undefined at those points.
Graph f
(
x
)
=√
x
−
1 to verify the results obtained:
Answer is [tex]y=\sqrt{x} -1[/tex]
