Question

verify the following functions are bijective
1. f:R to R f(x)=4x +3
2.g:R to R g(x)=(x^2)+1
​

Answer 1

Given:

1. f:R to R f(x)=4x +3

2.g:R to R g(x)=(x^2)+1

To find:

verify the functions are bijective.

Solution:

1)

$\bold{f(x)=4x+3}$

calculating the derivative of  the above method:

$f'(x)=4$

the value of  $x\geq 0$ when x=1 and -1 the value is equal to 1, -1 that's why it is not bijective.

2)

$\bold{g(x)=x^2+1}$

calculating the derivative of  the above method:

$g'(x)= 2x$

the value of  $x\geq 0$ when x=$+\infty$ and $-\infty$the value is equal to $+\infty$ and $-\infty$ that's why it is bijective.