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In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer. f defined from R to R defined by f(x) = 3 - 4x

Q.7 In each of the following cases, state whether the function is one-one, onto or
bijective. Justify your answer.

(i) f: R\rightarrow R defined by f(x) = 3 -4x

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f: R\rightarrow R

f(x) = 3 -4x

Let  there  be  (a,b) \in R  such that f(a)=f(b)

                                                          3-4a = 3 -4b

                                                               -4a = -4b

                                                                    a = b

\therefore f is one-one.

Let there be y \in R,    y = 3 -4x

                                    x = \frac{(3-y)}{4}

                                 f(x) = 3 -4x

Puting value of x,    f(\frac{3-y}{4}) = 3 - 4(\frac{3-y}{4})

                               f(\frac{3-y}{4}) = y

                           \therefore  f is onto.

f is both one-one and onto hence, f is bijective.

   

 

 

 

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