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f(x) there will be a different x.
c. Is it a one-to-one correspondence?
For a function to be a one-to-one correspondence it must be both one-
to-one and
onto. It must have a codomain equal to the range, and each element of
the domain
must map to only a single element in the range so based on exercise a
we can see that
is not onto therefore is not one-to-one correspondence. d. Find the
range of f
Range = {n ∈ Z | 6n+1 ∈
= {…, -11, -5, 1, 13, 19, …} Z} 3. (10 pts) f: R → R and g: R → R
are defined by the rules:
f(x) = x2 + 2 ∀
g(y) = 2y + 3 ∀ x ϵ R y ϵ R Find f ◦ g and g ◦ f
2
2
f ◦ g = f ( g ( y ) )=(2 y+ 3) +2=4 y +12 y +11
2
f ◦ g = 4 y +12 y +11 g ◦ f = g(f(x)) = g(x2 + 2)
=> g(x2 + 2) = 2(x2 + 2) + 3
=> 2x2 + 4 + 3 = 2x2 + 7
g ◦ f = 2x2 + 7