Functions: Let f:Nto Y be a function defined as f(x)=4x+3 where Y=\yin N,\… | AIEEE 2008 | Yukti Vault

Yukti Vault

AIEEE 2008 (Offline)Question 1

Let $f:N\to Y$ be a function defined as $f(x)=4x+3$ where $Y=\{y\in N,\ y=4x+3\text{ for some }x\in N\}$. Show that $f$ is invertible and its inverse is

Functions

$g(y)=\frac{3y+4}{4}$$g(y)=4+\frac{y+3}{4}$$g(y)=\frac{y+3}{4}$$g(y)=\frac{y-3}{4}$✓ Correct answer

Solution

$f$ is one-one and onto $Y$; $y=4x+3\Rightarrow x=\frac{y-3}{4}$, so $g(y)=\frac{y-3}{4}$.

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