Abolition of intermediaries' and 'Land ceiling act' are a part ofLet f : N → Y be a function defined as f (x) = 4x + 3, where, Y = {y ∈ N: y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse.:
Answers
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Checking for Inverse :-
f(x) = 4x + 3
Let f(x) = y
y = 4x + 3
y – 3 = 4x
4x = y – 3
x = ( − 3)/4
Let g(y) = ( − 3)/4
where g: Y → N
Now find gof :-
gof= g(f(x))
= g(4x + 3) = [(4 + 3) − 3]/4
= [4 + 3 − 3]/4
=4x/4
= x = IN
Now find fog :-
fog= f(g(y))
= f [( − 3)/4]
=4[( − 3)/4] +3
= y – 3 + 3
= y + 0
= y = Iy
Thus, gof = INand fog = Iy,
Hence, f is invertible
Also, the Inverse of f = g(y) = [ – 3]/ 4
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Checking for Inverse :-
f(x) = 4x + 3
Let f(x) = y
y = 4x + 3
y – 3 = 4x
4x = y – 3
x = ( − 3)/4
Let g(y) = ( − 3)/4
where g: Y → N
Now find gof :-
gof= g(f(x))
= g(4x + 3) = [(4 + 3) − 3]/4
= [4 + 3 − 3]/4
=4x/4
= x = IN
Now find fog :-
fog= f(g(y))
= f [( − 3)/4]
=4[( − 3)/4] +3
= y – 3 + 3
= y + 0
= y = Iy
Thus, gof = INand fog = Iy,
Hence, f is invertible
Also, the Inverse of f = g(y) = [ – 3]/ 4
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Hope It's Helpful.....:)