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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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