 #1
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 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.
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.