Question

show that f:R to R defined by f(x)=x+2 is a bijection also find f inverse(4)and {f inverse(x):2 lessthan or equal to x less than or equal to 3}.​

Answer 1

Answer

f:R

1

→(4,∞)

f(x)=x

2

+4

f(x

1

)=f(x

2

)

x

1

2

+4=x

2

2

+4

x

1

=x

2

f(x) is on-one.

f(x)=x

2

+4

y=x

2

+4

x

2

=y−4

x=

y−4

f(x)=x

2

+4

f(x)=(

y−4

)

2

+4

f(x)=y−4+4

f(x)=y

f(x) is onto function.

So,f(x) is bijective, Hence it is invertible

f(x)=x

2

+4

y=x

2

+4

y=x

2

−4

y=

x

2

−4

f

−1

(x)=

x−4