Question

For \(f(x)=4x+3\), where \(Y=\{y\in\mathbb{N}:y=4x+3\text{ for some }x\in\mathbb{N}\}\), what is the inverse function \(g:Y\to\mathbb{N}\)?

विकल्प

• \(g(y)=\frac{y+3}{4}\)

• \(g(y)=4y+3\)

• \(g(y)=\frac{y-3}{4}\)

• \(g(y)=\frac{4}{y-3}\)

Answer 1

From \(y=4x+3\), subtracting 3 and dividing by 4 gives \(x=\frac{y-3}{4}\). Therefore, \(g(y)=\frac{y-3}{4}\), with domain \(Y\) and codomain \(\mathbb{N}\).