Question

The function f: QQ defined by f (x)= 3x + 5, X EQ is (a) not one-one (b) not onto (c) one-one onto (d) none of these​

Answer 1

Answer:

one−one test of f:

Let x and y be two elements of the domain (Q), such that

f(x)=f(y)

⇒ 3+5=3y+5

⇒ 3x=3y

⇒ x=y

So, f is one-one.

Onto test of f:

Let y be in the co-domain (Q), such that f(x)=y

⇒ 3x+5=y

⇒ 3x=y−5

⇒ x=

3

y−5

∈ (domain)

∴ f is onto.

So, f is a bijection.

Hence, it is invertible.

Finding f

−1

:

Let f

−1

(x)=y ---- ( 1 )

⇒ x=f(y)

⇒ x=3y+5

⇒ x−5=3y

⇒ y=

3

x−5

So, f

−1

x=

3

x−5

From ( 1 ) ]