The function f :A to B defined by f(x) =4x + 7

Question

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Answer 1

Here, function f : A → B defined by , f(x) = 4x + 7, x∈R

Claim: f is one-one ? 

Consider,

f(x) = f(y)

4x + 7 = 4y + 7

4x = 4y

x = y

Therefore, function f is one-one. 

Now, 

Claim: f is onto

let, y ∈ B , such that

y = f(x)

y = 4x + 7

4x = y - 7

x = (y - 7)/4

Since, y∈B 

and x = (y - 7)/4 also belongs to B. 

i.e., x ∈ B 

Therefore, f is onto.