Question

Let f(x) = |x|, ????(x) = 2f(x), and h(x) = 1 / 2 f(x) for any real number x.

a. Write a formula for ????(x) in terms of |x| (i.e., without using f(x) notation).
b. Write a formula for h(x) in terms of |x| (i.e., without using f(x) notation).

Answer 1

g(x) = 2|x|

h(x) =
`(1)/(2)`|x|

Explanation:

If you have g(x)=2f(x) and h(x)=
`(1)/(2)`f(x), you can rewrite the expressions in terms of |x| as the following:

- For g(x)=2f(x) you have:

g(x) = 2|x|

-For h(x)=
`(1)/(2)`f(x), you have:

h(x) =
`(1)/(2)`|x|