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Joint Entrance Examination
Mathematics
Functions
Question 27
Question 27 of 162
Medium
MCQ
Let the domain of the function
f
(
x
)
=
log
3
log
5
(
7
−
log
2
(
x
2
−
10
x
+
85
)
)
+
sin
−
1
(
∣
3
x
−
7
17
−
x
∣
)
f(x)={\log }_{3}{\log }_{5}(7-{\log }_{2}({x}^{2}-10x+85))+{\sin }^{-1}(|\frac{3x-7}{17-x}|)
f
(
x
)
=
lo
g
3
lo
g
5
(
7
−
lo
g
2
(
x
2
−
10
x
+
85
))
+
sin
−
1
(
∣
17
−
x
3
x
−
7
∣
)
be
(
α
,
β
]
(\alpha ,\beta ]
(
α
,
β
]
. Then
α
+
β
\alpha +\beta
α
+
β
is equal to :
A
12
B
8
C
10
D
9
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Official solution
\[\& {x}^{2}-10x+85=\lambda \ \& \therefore \lambda >0\ldots \ldots \ldots \ldots .(1) \ \& \&7-{\log }_{2}\lambda >0\Rightarrow \lambda 0\Rightarrow \lambda From (A) \& (B), domain of function will be ( 3,6 ]\]
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