How is this type of piecewise function represented and calculated?

Question

How is this type of piecewise function as follows in the picture represented and calculated?

Use:

Clear["Global`*"]
f[x_] = Piecewise[{{Cos[(\[Pi] x)/2], x <= 0}, {f[x - 1] + 1, x > 0}}]

This prompt appears：

The process of calculating the corresponding function value is as follows: such as f[2]

In[5]:= Clear["Global`*"] f[x_] := Piecewise[{{Cos[([Pi] x)/2], x <= 0}, {f[x - 1] + 1, x > 0}}]
In[7]:= f[2]

Out[7]= 3 — csn899, Jun 05 '23 at 23:51
As a general rule, I tend to write any function definition using SetDelayed as a matter of course, unless I have a special reason not to do so (and add a ClearAll[functionName] before the definition as well). — MarcoB, Jun 06 '23 at 00:53

score 5 · Accepted Answer · answered Jun 06 '23 at 00:43

5

Clear["Global`*"]

f[x_?NumericQ] :=
 Piecewise[{{Cos[(π x)/2], x <= 0}, {f[x - 1] + 1, x > 0}}]

Plot[f[x], {x, -6, 10}]

answered Jun 06 '23 at 00:43

Bob Hanlon

2

What's the meaning of x_?NumericQ? – csn899 Jun 06 '23 at 02:27
2

It keeps the function from evaluating unless the argument is numeric. See the documentation for PatternTest – Bob Hanlon Jun 06 '23 at 02:32
@csn899 See https://mathematica.stackexchange.com/questions/18393/what-are-the-most-common-pitfalls-awaiting-new-users/26037#26037 – Michael E2 Jun 06 '23 at 17:42

1 Answers1