Question

1. The function f: R→ R defined by f(x) = 4* + 4x is​

Answer 1

Answer:

f:R→R

f(x)=4

x

+4

∣x∣

=

⎩

⎪

⎪

⎨

⎪

⎪

⎧

4

x

+4

x

,

2,

4

x

+4

−x

,

x>0

x=0

x<0

0∈R s.t there doesn't exist any x∈R

s. t f(x)=0

∴ f is not onto

Again let x

1



=x

2

⇒4

x

1



=4

x

2

⇒4

∣x

1

∣



=4

∣x

2

∣

⇒4

x

1

+4

∣x

1

∣



=4

x

2

+4

∣x

2

∣

Since 4

x

1

and 4

∣x

1

∣

are always positive.

∴f(x

1

)



=f(x

2

)

∴ f is one-one.

∴ f is one-one and into.