Question

Consider ∶ ℝ → ℝ defined by = 5 + 3 . Show that is a bijective function

Answer 1

Answer:

here your answer

Step-by-step explanation:

prove the function is surjective you must show that for any point “a” in the range there is a point “b” in the domain such that f(b)=a.

This is easily shown by letting a=3x-5 and therefore b must be (a+5)/3. Since this is a real number it is in the domain.

To prove the function is injective you must show if f(a)=c and f(b)=c then a=b.

Let f(a)=c and f(b)=c -> c=3a-5 and c=3b-5 -> 3b-5=3a-5 -> 3b=3a -> b=a

Since it is both injective and surjective we can say that f(x) is a bijection from R to R