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Home » Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by f(x) = (x-2)/(x-3). Is f one-one and onto? Justify your answer. Solution: A = R – {3} and B = R – {1}
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by f(x) = (x-2)/(x-3). Is f one-one and onto? Justify your answer. Solution: A = R – {3} and B = R – {1}
CBSE | Class 12 | Maths | NCERT | Relations and Functions
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by f(x) = (x-2)/(x-3). Is f one-one and onto? Justify your answer. Solution: A = R – {3} and B = R – {1}

f : A → B characterized by f(x) = (x-2)/(x-3) Let (x, y) ∈ A then, at that point

????(????) =

???? − 2

???? − 3

???????????? ????(????) =

???? − 2

???? − 3

For f(x) = f(y)

Once more, f(x) = (x-2)/(x-3)

or on the other hand y = f(x) = (x-2)/(x-3)

y = (x-2)/(x-3) y(x – 3) = x – 2 xy – 3y = x – 2 x(y – 1) = 3y – 2

or on the other hand x = (3y-2)/(y-1)

Presently, f((3y-2)/(y-1)) =

3????−2−2

????−1

3????−2−3

????−1

f(x) = y

Consequently, f is onto work.


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