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Consider the function
MATHEMATICS · Multi-part · GCSE · Mathematics · Algebra · Algebra
Problem
Consider the function
p
t
(
x
)
=
4
x
−
x
2
+
1
x
−
t
p_t(x)=\sqrt{4x-x^{2}}+\dfrac{1}{x-t}
p
t
(
x
)
=
4
x
−
x
2
+
x
−
t
1
, where
t
∈
R
t\in\mathbb R
t
∈
R
. (i) Obtain the domain of
p
t
p_t
p
t
in terms of
t
t
t
. (ii) Find all real values of
t
t
t
for which the domain of
p
t
p_t
p
t
is exactly
(
0
,
4
)
∖
{
t
}
(0,4)\setminus\{t\}
(
0
,
4
)
∖
{
t
}
. Present a complete algebraic argument.
Related theory
Non-Linear Equations
Algebra
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