Plot3D[x^2Sin[10 y^2]-x Log[x],{x,0,3},{y,1,2}]

f[x_]:=x^2-x Log[x]

?f

Plot[f[x],{x,0,3}]

f[y_]:=y^2-y Log[y]

f[3]:=y^2-y Log[y]

f[z]:=y^2-y Log[y]

f[a]

f[4]

f[4.]

Log[E]

f[E]

f["paolo"]

f[f]

f[]

?f

f[1,2]

f[a_,b_]:= a+b

f[1,2]

f[x]

?f

f[a_,b_]:=a b

?f

f[E]

f[E 1.]

f[E]//N

N[f[E],100]

f[z]

f'[z]

D[f[x],x]

Integrate[f[z],z]

Integrate[f[z],{z,E,E^2}]

Solve[f[z]==2.1,z]

NSolve[f[z]==2.1,z]

NSolve[(z^2)-z Log[z]==2.1,z,Reals]

rule=FindRoot[f[x]==2.1,{x,1}]

y =f[x]/.rule

Abs[y-2.1]/2.1

?f

f[3+2I]

f[x^2(3+2I)Sin[y]]

f[{1,a,34}]

{1,a,34}^2 -{1,a,34}Log[...]

?f

f[n_Integer]:= n!

f[4.]

f[4]

?f

f[z_Complex]:=Abs[z]

?f

Map[
f,
{6,6+0I,6+0.I}
]

g[x_List]:=Length[x]

{g[],
g[{1,2,3}],
g[1,2,3]}

h[x_List]:=Length[{x}]

{h[],
h[{1,2,3}],
h[1,2,3]}

r[x_]:=Length[{x}]

{r[],
r[{1,2,3}],
r[1,2,3]}

t[{x_}]:=Length[{x}]

{t[],
t[{1,2,3}],
t[1,2,3]}

Clear[g]

(* g on Integers   factorial[n+1]
 g on Reals      -identity
 g on Lists      length *)

Head[{4.3}]

Clear[h]

h[x_]:=
If[ToString[Head[x]]=="Integer",Factorial[x+1],
If[ToString[Head[x]]=="Real",-x,
If[ToString[Head[x]]=="List",Length[x]
]
]
]

Map[h,{Pi,4,4.,{Pi},{4.}}]//ColumnForm

Clear[h]

h[x_]:=
If[Head[x]===Integer,Factorial[x+1],
If[Head[x]===Real,-x,
If[Head[x]===List,Length[x]
]
]
]

Map[h,{Pi,4,4.,{Pi},{4.}}]//ColumnForm

?Switch

g[x_]:=
Switch[Head[x],
Integer,Factorial[x+1],
Real,-x,
List,Length[x],
_, 
]

Map[g,{Pi,4,4.,{Pi},{4.}}]//ColumnForm