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In following case, state whether the functions are one-one, onto or bijective. And justify the answer.

f: R→ R defined by f(x)=3−4x

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An Intiative by Sri Chaitanya

Only One-one

Only Onto

bijective

none

answer is C.

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Detailed Solution

Given that,
f: R→ R defined by f(x)=3−4x
Suppose

x_{1}, x_{2} \in R

As,

f (x_{1}) = f (x_{2})

\Rightarrow 3 - 4 x_{1} = 3 - 4 x_{2}

\Rightarrow - 4 x_{1} = - 4 x_{2}

\Rightarrow x_{1} = x_{2}

Therefore, we can said that the given function is one-one function.
In R, for any real number (y),
Here,

\frac{3 - y}{4}

in R as,

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

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

= y

So, the given function is onto.
As, the function is both one-one and onto. So it is bijective.
Option 3 is correct.

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