Is function argument required to be enclosed in parentheses?

No, function argument is not required to be enclosed in parentheses.

"ISO 80000-2 Quantities and Units - Mathematics" specifies that:

• Parentheses are required, if the function identifier is a single letter, like f(θ).
• Parentheses are required, if the function argument is a multiple terms, like sin(a+b).
• Parentheses may be omitted, if the function identifier has multiple letters and the argument is a single term. In this case, a space is required between the identifier and the argument, like sin ωt.

The <mi> tag is rendered correctly with an extra space between the identifier and the argument if parentheses are omitted. For examples:

<math><mi>sin</mi><mo>⁡</mo><mi>θ</mi>
  <mo>=</mo><mi>cos</mi><mo>⁡</mo>
  <mo>(</mo><mn>0.5</mn><mi mathvariant="normal">π</mi><mo>-</mo><mi>θ</mi>
  <mo>)</mo></math>
    $\sin \theta =\cos (0.5\mathrm{\pi }-\theta )$

<math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo>
  <mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>
    $f\left(x\right)=ax+b$

⇒ Function Arguments - "mrow" Tag

⇐ Function Arguments - "Invisible Apply Function" Operator U+2061

⇑ ISO 80000-2 Quantities and Units - Mathematics

⇑⇑ MathML (Mathematical Markup Language)