Answer:
Explanation:
To check whether the given functions are bijections or not.
[tex]a) f(x) = -3x+4\\[/tex]
For x1 and x2 if [tex]f(x1)=f(x2)\\-3x1+4 =-3x2+4\\x1=x2[/tex]
Hence one to one
For any given f(x) we have
[tex]x=\frac{4-f(x)}{3}[/tex] hence co domain = range. Thus onto
Hence bijection.
b) [tex]f(x) = -3x^2+7[/tex]
Let x =a and x=-a
We get
[tex]f(a) = -3a^2+7\\f(-a) = -3a^2+7\\f(a) = f(-a)[/tex] for all a
Hence f is not one to one
Not bijective.
