Question

Determine whether each of these functions is a bijection from R to R.

a) f(x) = -3x+4

b) f(x) = -3x^2 +7

Answer 1

Step-by-step explanation:

To check whether the given functions are bijections or not.

`a) f(x) = -3x+4\\`

For x1 and x2 if
`f(x1)=f(x2)\\-3x1+4 =-3x2+4\\x1=x2`

Hence one to one

For any given f(x) we have

`x=(4-f(x))/(3)` hence co domain = range. Thus onto

Hence bijection.

b)
`f(x) = -3x^2+7`

Let x =a and x=-a

We get

`f(a) = -3a^2+7\\f(-a) = -3a^2+7\\f(a) = f(-a)` for all a

Hence f is not one to one

Not bijective.