Question

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.:​

Answer 1

${ \huge{\boxed{\tt {\color{red}{Answer}}}}}$

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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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${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

Answer 2

$\huge{\orange{\underline{\purple{\mathscr{Solution}}}}}$

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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.....:)