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Question

f:AB is a function satisfying 3f(x)+2x=4. Then the domain and range of f are

A
A={xR:1<x<};
R(f)={xR:2<x<4}
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B
A={xR:3<x<};
R(f)={xR:0<x<log34}
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C
A={xR:2<x<};
R(f)={xR:<x<log34}
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D
A={xR:2<x<};
R(f)={xR:<x<log341}
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Solution

The correct option is C A={xR:2<x<};
R(f)={xR:<x<log34}
3f(x)+2x=4
3f(x)=42x
f(x)=log3(42x)

For domain
42x>0
2x<22
x<2 [For a>1,ax<ayx<y]
x>2
Domain ={xR:2<x<}


Now, 2<x<
<x<2
0<2x<4
0<42x<4
Since, logax is strictly increasing for a>1, we get
<log3(42x)<log34
R(f)={xR:<x<log34}

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