Determine whether each of these functions is a bijection from \(\mathbf{R}\) to \(\mathbf{R}\).

a) \(f(x)=2 x+1\)

b) \(f(x)=x^{2}+1\)

c) \(f(x)=x^{3}\)

d) \(f(x)=\left(x^{2}+1\right) /\left(x^{2}+2\right)\)

Equation Transcription:

Text Transcription:

R

f(x)=2x+1

f(x)=x^2+1

f(x)=x^3

f(x)=(x^2+1/(x^2+2)

Solution:

Step 1 :

We have to check weather the following function are bijection from .

given functions are

(a)

Ans :

First check the given function is one-one

Such that

.’. The given function is one-one.

next we to check the onto

In the given function the range is real numbers

.’. The function is onto

Hence the function is bijective.