Is the function f(x) = √ x + 3 − 1 a one to one function?

Question

Is the function f(x) = √x + 3 − 1 a one-to-one function? How can you tell? If it is, find the inverse function. Label both functions.

Answer 1

Let f(a) = √a + 3 -1 and f(b) = √b + 3 - 1

If f(a) = f(b) then √ a +3 - 1 = √b + 3 - 1; √a + 3 = √b + 3; a + 3 = b + 3. So, a = b

This is prove that f(x) is one-to-one in its domain [- 3, ∞)