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Question

Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1

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Solution

Injectivity of f:
Let x and y be two elements of the domain (Q), such that
f(x)=f(y)
3x + 5 =3y + 5
3x = 3y
x = y
So, f is one-one.

Surjectivity of f:
Let y be in the co-domain (Q), such that f(x) = y

3x+5=y3x=y-5x=y-53Q domain

f is onto.
So, f is a bijection and, hence, it is invertible.

Finding f -1:
Let f-1x=y ...1x=fyx=3y+5x-5=3yy=x-53So, f-1x=x-53 [from 1]

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