Question
For the function $f: A \rightarrow B, f(x)=4 x-3 ; R_f=\{9,13,17,25\}$ then find $D_f$.
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Answer
$f: A \rightarrow B, f(x)=4 x-3, R_f=\{9,13,17,25\}$
$f(x)=9 \therefore 9=4 x-3, \therefore 12=4 x \therefore x=3$
$f(x)=13 \therefore 13=4 x-3 \therefore 16=4 x \therefore x=4$
$f(x)=17 \therefore 17=4 x-3 \therefore 20=4 x \therefore x=5$
$f(x)=25 \therefore 25=4 x-3 \therefore 28=4 x \therefore x=7$
Hence, $D_f=\{3,4,5,7\}$
$f(x)=9 \therefore 9=4 x-3, \therefore 12=4 x \therefore x=3$
$f(x)=13 \therefore 13=4 x-3 \therefore 16=4 x \therefore x=4$
$f(x)=17 \therefore 17=4 x-3 \therefore 20=4 x \therefore x=5$
$f(x)=25 \therefore 25=4 x-3 \therefore 28=4 x \therefore x=7$
Hence, $D_f=\{3,4,5,7\}$
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