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.