Formulas for computing composite function

  • Thread starter rxh140630
  • Start date
  • #1
37
6

Homework Statement:

Let f and g be two functions defined as follows:

[itex] f(x) = \frac{x+|x|}{2}[/itex]

[itex] g(x) = \begin{cases}
x \text{ for x < 0} \\
x^2 \text{ for x ≥ 0}

\end{cases} [/itex]

Find a formula, or formulas, for computing the composite function h(x) = f[g(x)]

Relevant Equations:

f ο g = f[g(x)]
h(x) = 0 for x ≤ 0
h(x) = x^2 for x>0

But my book says

h(x) = 0 for x<0
h(x) = x^2 for x≥0

Can my solution (the first one) work as well? Because the actual function value at x = 0 is zero. I feel like my solution is more elegant.
 

Answers and Replies

  • #2
anuttarasammyak
Gold Member
333
158
Yes, the both give the same result.
 
  • Like
Likes rxh140630
  • #3
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
14,358
6,729
h(x) = 0 for x ≤ 0
h(x) = x^2 for x>0

But my book says

h(x) = 0 for x<0
h(x) = x^2 for x≥0
These define the same function ##h##. To see this, you can ask at what points do the function values differ?
 
  • Like
Likes rxh140630
  • #4
37
6
These define the same function ##h##. To see this, you can ask at what points do the function values differ?
They do not differ because x^2 at x=0 = 0, if we choose to use the authors definition.

Since they do not differ then they must be the same.
 
Last edited:

Related Threads on Formulas for computing composite function

  • Last Post
Replies
1
Views
697
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
962
  • Last Post
Replies
2
Views
765
Replies
1
Views
601
Top