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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 $f(x) = 3 -4x$

Answers (1)

S seema garhwal

$f: R\rightarrow R$

$f(x) = 3 -4x$

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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