Defining Compound Function

1,046

If $f(x) = (x+x)$ and $g(x) = 2(x-5)$, and we have the compound function $g(f(x))$, how can we "define what the resulting function does"?

What the resulting function does is that it maps $f(x)\to \mathbb{R}$, that is, the new function, called a "composition of two functions", has the range of a function as its domain. Other than that, it retains all other functional properties of itself.

In this case, $g(f(x))$ maps from $f(x)\to \mathbb{R}$, so it has the range of $f(x)$ as its domain. And the function hence gets modified in a similar fashion. Since $g(x) = 2(x-5)$, so by logic, we conclude that $g(f(x)) = 2[f(x)-5] = 2[(x+x)-5]$.

Share:
1,046

Related videos on Youtube

M-R
Author by

M-R

Updated on December 14, 2020

Comments

  • M-R
    M-R almost 3 years

    If $f(x) = (x+x)$ and $g(x) = 2(x-5)$, and we have the compound function $g(f(x))$, how can we "define what the resulting function does"?

    It's obvious what is happening, but I'm not quite sure how this question is asking and how it would be laid out.

    Perhaps, $g(x) = 2((x+x)-5)$

    • SchrodingersCat
      SchrodingersCat almost 8 years
      Is the edit alright? Please check.
    • M-R
      M-R almost 8 years
      @Aniket It's no longer what the exercise question states, but I don't suppose it makes much of a difference.
    • SchrodingersCat
      SchrodingersCat almost 8 years
      Why? Any problem?
    • M-R
      M-R almost 8 years
      @Aniket It's all good. x