Question

how to say a domain as part of the function verbally

Answer 1

If you mean “how do I say the domain when I read a function aloud,” here are short, clear ways to do it and some examples.

Basic phrasing
- f: D → R — read as “f is a function from D to R” or simply “f from D to R.”
- domain(f) = D — read as “the domain of f is D.”
- f(x) = ... , x ∈ D — read as “f of x equals … for x in D” or “where x is in D.”
- f: D → R, x ↦ f(x) — read as “f is a map from D to R sending x to f of x.”

Common symbol pronunciations
- ∈ — “is in” or “belongs to”
- ∉ — “is not in”
- ∪ — “union”
- ∩ — “intersection”
- \ or \{...} — “minus” or “excluding” (e.g. R \ {0} = “R minus zero”)
- → — “to” or “maps to” (use “maps to” when reading x ↦ f(x))
- ↦ — “maps to” (read x ↦ f(x) as “x maps to f of x”)

Examples
- f: [0,1] → R, f(x) = x^2
- “f is a function from the closed interval zero to one to the real numbers, defined by f of x equals x squared.”
- Or: “f of x equals x squared for x in the interval zero to one.”
- g: R \ {0} → R, g(x) = 1/x
- “g is a function from R minus zero to R, given by g of x equals one over x.”
- Or: “g of x equals one over x for x not equal to zero.”
- h: N → {0,1}, h(n) = ...
- “h maps the natural numbers to the set zero one.”
- k(x) = sqrt(x), x ≥ 0
- “k of x equals the square root of x, defined for x greater than or equal to zero.”

Formality tip
- In casual speech say “f from D to R” or “f of x equals … for x in D.”
- In formal or lecture settings prefer “f is a function from D to R, defined by …” or “let f: D → R be defined by …”

If you want, give an example function and I’ll show a few natural ways to read it aloud.