Question

Define a function f : R → R by the formula

f(x) = 2x − 8.


Prove that f is one-to-one.
Let a, b is in R, and suppose that
f(a) = f(b).
Then
2a − 8 =

Answer 1

We are given a function f(x) = 2x - 8 and a condition that f (a) = f (b). We are then asked the next terms of 2a - 8 = ______.

Now, we have to think that the parent function is f(x) = 2x - 8 and f (a) = f (b). This means the value of the function f(a) is if a is substituted to x:

f (a) = 2a - 8, same goes for f (b):

f (b) = 2b - 8.

Since we have a condition that f(a) = f (b), then,

2a - 8 = 2b - 8.

If we simplify further,

2a = 2b - 8 + 8
( 2a = 2b ) / 2

the equation becomes:

a = b; this proves that f is a one-to-one function.