College Algebra

Question

F is a function that takes a real number x performs these four steps in the order given :

1. multiply by -1

2. add 2

3. take the square root

4. take the reciprocal

find an expression for f(x)

state the domain of f

Answer 1

A function transforms the input x values into the output y values according to some rule:

x ---> f(x) ---> y

The rule for this case is:

1. multiply (the input x) by -1: -1·x = -x

2. add 2: -x + 2

3. take the square root: √(-x+2)

4. take the reciprocal: 1/√(-x+2)

f(x) = 1/√(-x+2)

The domain is x < 2. The reason is that you can't take the square root of a negative number, so if x > 2, then -x+2 would be negative. Also, it can't be x = 2, since that would make the -x+2 equal to zero and you can't divide by zero.