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I have two functions,

$g(x) = 4x^3$, domain $0<x<0.5$

$h(x) = \frac{1}{2}((2x-1)^3+1)$, domain $0.5\le x<1$

which I derived from:

$g(x) = ((2x)^3)/2$, domain $0<x<0.5$

$h(x) = ((2(x-0.5))^3)/2+0.5$, domain $0.5\le x<1$

I want to combine g(x) and h(x) info one function, f(x). If it helps, h(x) is derived from g(x). Here is a graph of g(x) and h(x). h(x) is g(x), [reflected] or [rotated $\pi$ radians] about $(0.5, 0.5)$.

I have looked at other questions related, such as this, but I wasn't sure how to apply the solution to this scenario because my functions didn't have two parameter. How can I combine these two into one function f?

$f(x)=?$

Community
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Dave
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  • @Dave: How about $f(x) = 4x^3(u_0(x) - u_\frac{1}{2} (x)) + \dfrac{1}{2} ((2x -1 )^3+1)u_1(x)$. Plot this and your piecewise one and see what you get. – Moo Dec 23 '15 at 22:47
  • The definition of $h(x)$ in your post does not match the graph. – Dave Radcliffe Dec 23 '15 at 22:51

1 Answers1

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Hint :

Both are cubic functions:

One thing you may try is $$f(x) = Ag(x) + Bh(x)$$

Evaluate f(x) in those interval ends and get the value of A and B. I have not tried but should work.

Satish Ramanathan
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