Question

If f: N → Y be a function defined as f(x) = 4x + 3, Where Y = {y ∈ N: y = 4x+ 3 for some x ∈ N} then function is

पर्याय

• one – one

• onto

• invertible

• into

Answer 1

invertible

Explanation:

Consider an arbitrary element y of Y.

By the definition of Y, y = 4x + 3, or some 'x in the domain N.

This shows that x = `((y - 3))/4`.

Define g(x) Y→ N by g(y) = `((y - 3))/4`.

Now g of (x) = g(f(x)) = g(4x + 3)

= `((4x + 3 - 3))/4` = x and f(g(y)) = f(g(x))

= `f(((y - 3))/4) = (4(y - 3))/L_1 + 3`

= y – 3 + 3

= y.

This show that of = I_N, and fog = I_y, which implies that 'f' is invertible and 'g' is the inverse of f.