Menu Close

If-f-A-B-given-by-3-f-x-2-x-4-is-a-bijection-then-find-A-and-B-if-possible-

Tinku Tara 0 Comments
Pin




Question Number 13283 by Tinkutara last updated on 17/May/17
If f : A → B given by 3^(f(x)) + 2^(−x) = 4 is a bijection, then find A and B if possible.
Iff:A→Bgivenby3f(x)+2−x=4isabijection,thenfindAandBifpossible.
Answered by 433 last updated on 17/May/17
f(A)=B 3^(f(x)) =4−2^(−x) f(x)=((ln (4−2^(−x) ))/(ln 3)) A={4−2^(−x) >0}={4>2^(−x) }= {2^2 >2^(−x) }={2>−x}={x>−2}=(−2,+∞) x>−2⇔−x<2⇔0<2^(−x) <4 ⇔−4<−2^(−x) <0⇔0<4−2^(−x) <4 ⇔−∞<ln (4−2^(−x) )<ln 4 ⇔^(ln 3>0) −∞<((ln (4−2^(−x) ))/(ln 3))<((ln 4)/(ln 3)) B=(−∞,((ln 4)/(ln 3)))
f(A)=B3f(x)=4−2−xf(x)=ln(4−2−x)ln3A={4−2−x>0}={4>2−x}={22>2−x}={2>−x}={x>−2}=(−2,+∞)x>−2⇔−x<2⇔0<2−x<4⇔−4<−2−x<0⇔0<4−2−x<4⇔−∞<ln(4−2−x)<ln4⇔ln3>0−∞<ln(4−2−x)ln3<ln4ln3B=(−∞,ln4ln3)

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *