Question

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

Answer 1

Answer:

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

$x=\frac{4-f(x)}{3}$ 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.