pattern matching - Is there any way to use head of Real and Integer altogether?

Is there any way to use the head of Integer and Real together like below? The below is not right, I know that, it is just for showing my thought.

f[x_(Integer||Real)] := x^2

The reason I ask this is because I need a function that receives an argument which is either integer or real.

Answer

To match your literal request you need Alternatives rather than Or.
Either x : (_Integer | _Real) or x_Integer | x_Real will work.

Following what Szabolcs and "Guess who it is" wrote you might define a realQ like so:

realQ = NumericQ[#] && Im[#] == 0 &;

f[x_?realQ] := x^2

f /@ {1, Pi, 1.3, 2/3, x^2, 7.1 - 2.8 I}

{1, π^2, 1.69, 4/9, f[x^2], f[7.1 - 2.8 I]}

Of note for those who are comfortable using undocumented functions:

Internal`RealValuedNumericQ /@ {1, Pi, 1.3, 2/3, x^2, 7.1 - 2.8 I}

{True, True, True, True, False, False}

There is also Internal`RealValuedNumberQ which passes only explicit numbers:

Internal`RealValuedNumberQ /@ {1, Pi, 1.3, 2/3, x^2, 7.1 - 2.8 I}

{True, False, True, True, False, False}