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Let f:N\rightarrow Y be a function defined as

f(x)=4x+3   where  y= \left \{ y\: \in\: N \: :y= 4x+3\: for\: some\: x\: \in\: y\right \}

Show that f is invertible and its inverse is

  • Option 1)

    g\left ( y \right )= \frac{y-3}{4}

  • Option 2)

    g\left ( y \right )= \frac{3y+4}{3}

  • Option 3)

    g\left ( y \right )=4+ \frac{y+3}{4}

  • Option 4)

    g\left ( y \right )= \frac{y+3}{4}

 

Answers (2)

As we learnt in

Bijective Function -

The function which is both one-one and onto is Bijective Function.

-

 

 f(x) = 4x + 3

Let y = 4x + 3

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

Correct option is 1.

 


Option 1)

g\left ( y \right )= \frac{y-3}{4}

This is the correct option.

Option 2)

g\left ( y \right )= \frac{3y+4}{3}

This is an incorrect option.

Option 3)

g\left ( y \right )=4+ \frac{y+3}{4}

This is an incorrect option.

Option 4)

g\left ( y \right )= \frac{y+3}{4}

This is an incorrect option.

Posted by

Sabhrant Ambastha

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