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Let the function be defined by
MATHEMATICS · Subjective · GCSE · Mathematics · Graphs · Graphs
Problem
Let the function
f
:
[
−
2
,
3
]
→
R
f:[-2,3]\to\mathbb R
f
:
[
−
2
,
3
]
→
R
be defined by
f
(
x
)
=
x
2
−
4
x
+
1
f(x)=x^{2}-4x+1
f
(
x
)
=
x
2
−
4
x
+
1
. (i) Rewrite
f
(
x
)
f(x)
f
(
x
)
in completed–square form. (ii) Using the result of part (i), determine the least value of
f
(
x
)
f(x)
f
(
x
)
on the interval
[
−
2
,
3
]
[-2,3]
[
−
2
,
3
]
. (iii) Hence find the range of the function
f
f
f
.
Related theory
Linear Inequalities
Algebraic Manipulation
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