Question

A function f : R Arrow R defined by f (x) = 3 x/5 + 2, x € R. Show that f is one - one and onto function. Hence find f^-1.​

Answer 1

Answer:

ANSWER

It is given that f:R⋅→R⋅ is defined by f(x)=

x

1

.

One-one.

f(x)=f(y)

⇒

x

1

=

y

1

⇒x=y

∴f is one-one.

Onto:

It is clear that for y∈R⋅, there exists x=

y

1

∈R⋅ (Exists as y



==0) such that f(x)=

y

1

1

=y

∴f is onto.

Thus, the given function (f) is one-one and onto.

Now, consider function $$g: N \rightarrow R\cdot $$ defined by

g(x)=

x

1

we have,

g(x

1

)=g(x

2

)⇒

x

1

1

=

x

2

1

⇒x

1

=x

2

⇒g is one-one.

Further, it is clear that g is not onto as for 1.2∈R⋅ there does not exit any x in N such that g(x)=

1.2

1

Hence, function g is one-one but onto.

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