Mathematica Notes: Input & Define a Function

Input

$\frac{a}{c}$
Press [Ctrl]+[/]
$x^a$
Press [Ctrl]+[^]
$\sqrt{x}$
Press [Ctrl]+[@]

Define a function

$f(x)=x^2+x+1$

Input:
f[x_] := x^2 + x + 1
f[1]
Output:
3

What difference between f[x_]:= and f[x_]= ?

:= means delayed assignment, the value will recompute everytime it needed.
= means assign value immediately
** =. means clear assignment

What difference between f[x_] and f[x] ?

input:
f[x_] := x^2 + x + 1
f[1]
g[y] := x^2 + x + 1
g[1]

output:
3
g[1]