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8/17/2019 Stp - 2 (Function) - s
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IIT - ian’s PACE ; ANDHERI / DADAR / CHEMBUR / THANE ; Tel : 26245223 / 09 ; .www.iitianspace.com
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B A T C H : 2 01 7 STP - 2 FUN CT IO N ) T IM E : 15 M in .
1. (C)
We must have 0 < 2 + e3{x} 1 or e2 2 + e3{x} e3
– 2 < e3{x} – 1 or e2 – 2 e3{x} e3 – 2
x or )2e(n3
1}x{)2e(n
3
1 32 l l
Hence
)2e(3
1n),2e(n
3
1nUx 32
Inl Ans. ]
2. (B)
f (x) = | Ax + c | + d
g (x) = – | Ax + u | + v
figure is parallelogram and diagonals bisect each other
A
u +
A
c = 3 + 1;
A
cu = – 4 Ans. ]
3. (C)
log10
(–x) = |x|log10
log10 (–x) = )x(log10 x < 0
let y = log10
(–x), then y – y = 0 i.e y ( y – 1) = 0
i.e y = 0 or y – 1 = 0
i.e y = 0 or y = 1
i.e log10
(–x) = 0 or log10
(–x) = 1
i.e –x = 1 or –x = 10
i.e x = –1 or x = –10
Thus there are two solutions.
8/17/2019 Stp - 2 (Function) - s
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IIT - ian’s PACE ; ANDHERI / DADAR / CHEMBUR / THANE ; Tel : 26245223 / 09 ; .www.iitianspace.com
4.99
(A)
For domain of f(x) = )x4(cos3 1 , we must have
cos –1 4x 3
4x
2
1 x
8
1 .......(1)
Also –1 4x 1 4
1x
4
1
........ (2)
From (1) and (2), we get x
8
1,
4
1]
5. A )
We must have [x] =
x x x x
2
[x]{x} + [x] ( [x] + {x}) = 2{x} ( [x] + {x} )
[x]2 = 2{x}2 {x}2 = 2
][ 2 x
0 < 2
][ 2 x