IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

neeraj_agarwal_1990

If f:A--->B given by 3^f(x)+2^-x=4 is a bijection , find A and B...

(answer was none of these)

elastiboysai

i guess u forgot the options

neeraj_agarwal_1990

i thought why to write options if answer is none of these!!

spideyunlimited

0 and 1?
not sure

nadeemoidu

The function a^x

can take values from $( 0 , \infty)$ .

So in the given function , each of the terms can take the values from ( 0 , 4)

$0 < 3^{f(x)} < 4 \\and \\ 0 < 2 ^{-x} <4$

Taking log ,

$-\infty < f(x) log3 < log4$ and $-\infty < -x log2 < log4$

$-\infty < f(x) < log_3 4$ and $-2 < x <\infty$

$A = ( - 2 ,\infty ) \\ B= (-\infty , log_3 4)$

neeraj_agarwal_1990

thanx a lot man!

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