Question

What are the domain and range of the real-valued function f(x)=-3- /4x-12

Answer 1

I’m not certain how to read "f(x) = -3- /4x-12". Could you confirm the exact formula? Common possibilities and their domain/range:

1) If f(x) = -3 - √(4x − 12)
- Domain: 4x − 12 ≥ 0 → x ≥ 3 (i.e. [3, ∞))
- Range: √(...) ≥ 0 so f(x) ≤ −3. At x = 3, f = −3, and as x → ∞, f → −∞, so range = (−∞, −3]

2) If f(x) = -3 - |4x − 12|
- Domain: all real numbers (−∞, ∞)
- Range: same as above, (−∞, −3]

3) If f(x) = -3/(4x − 12)
- Domain: 4x − 12 ≠ 0 → x ≠ 3
- Range: y ≠ 0 (this rational function can produce any nonzero real)

4) If f(x) = -3 - (1/4)x - 12 (i.e. -3 - (1/4)x - 12)
- Simplifies to f(x) = -15 - x/4
- Domain: all real numbers
- Range: all real numbers

Tell me which of these (or paste the function exactly using parentheses or a sqrt/abs symbol) and I’ll give a short, final answer.