Question 424499: Q1:Let u belong to a and v belong to B where A={0,1,2,3,4,} and B={1,3,5,7,9}.
Let Q maps A > B such that v=u^2-1
Let D maps B > A such that v=v-3
Hint: Beware of co domains
Find the range of Q
Find Q
Find D
Determine whether Q is injective
Determine whether D is surjective
Determine whether Q has an inverse
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q1:Let u belong to a and v belong to B where A={0,1,2,3,4,} and B={1,3,5,7,9}.
Let Q maps A to B such that v=u^2-1
Let D maps B to A such that u=v-3
Hint: Beware of co domains
Find the range of Q:::: {v|u^2-1 where u = 0,1,2,..,4) = {-1,0,3,8,15}
Find Q::: Q = {-1,0,3,8,15}
Find D::: D = {v|v= v-3} = {-2,0,2,4,6}
----
Determine whether Q is injective: (one-to-one): yes
Determine whether D is surjective: (onto): no
Determine whether Q has an inverse:: u = sqrt[v+1]
=========================
Cheers,
Stan H.
|
|
|
