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

f[a]

f[Pi]

f[3]

f[3.]

f[3]//N

N[f[3],50]

f'[x]

f''[t]

D[f[z],z]

Integrate[f[t],t]

Integrate[f[t],{t,0,3}]

NIntegrate[f[t],{t,0,3}]

FindRoot[f[z]==2,{z,1}]

FindRoot[f[z]==3z-1,{z,1}]

p[a_]:=a^12-a^6-a^5+20 a +1

NSolve[p[t]==3,t]

?p

{p[i],p["abc"],p[{1,2,z}],p[I],p[p]}//ColumnForm

p["abc"]//FullForm

p["abc"]//Head

g on Integers : factorial
g on Reals : identity
g on Lists : Length

Head[3]

Head[3.]

Head[{1,2,3}]

g[x_]:=
If[Head[x]===Integer,x!,
If[Head[x]===Real,x,
If[Head[x]===List,Length[x]]
]
]

g[{1,2,3}]

?Switch
?Which

IntegerQ[3]

?IntegerQ

NumberQ[3]

NumberQ[3+I]

NumberQ[Pi]

Head[Pi]

Head[Pi//N]

NumberQ[I]

Clear[f]

f[n_Integer]:=n!

f[x_Real]:=x

f[x_List]:= Length[x]

?f

f[{1,2,3,4},{1,2,34}]

f[Pi]

f[x_]:=x^2

Head[E]

f[E]

?f

Integer, Real, Complex, List, Symbol,String

Head["abc"]

?String

Clear[f]

f[x_]:= Sin[x]/x

Plot[f[t],{t,-5,5}]

f[0]

Limit[f[t],t->0]

f[0]:=Limit[f[t],t->0]

?f

f[0.]

Clear[f]

f[0.]:=Limit[f[t],t->0]

?f

f[0]

f[0]:=Limit[f[t],t->0]

?f

f[0.]

(*  f[x_]:=Limit[Sin[t]/t,t->x]  *)

Clear[f]

f[t_]:=Sin[t]/t

f[0.]=Limit[f[t],t->0]

?f

(*  f[t_]:=f[t]=Limit[ ... ]  *)

?Sinc

Plot[f[t],{t,-10,10}]

Clear[f,fact]

fact[n_]:=n*fact[n-1]

fact[3]

?fact

fact[0]=1;

fact[100]

?fact

fact[-1]

fact[x_/;0≤x≤1]:=1

?fact

fact[x_/;x<0]:=-fact[-x]

fact[2.5]

ff[x_]:=x^2

ff[x_Integer]:=x

?ff

ff[4]

ff[4.]

Clear[gg]

gg[x_Integer]:=x

gg[x_]:=x^2

?gg

gg[4]

gg[4.]

Clear[ff,gg]

ff[x_/;x<4]:=x

ff[x_/;x>2]:=x^2

gg[x_/;x>2]:=x^2

gg[x_/;x<4]:=x

Plot[ff[t],{t,0,6}]

Plot[gg[t],{t,0,6}]

?ff

?gg