Question

What are the domain and range of the function f(x)=2squared x+1

Answer 1

Do you mean f(x) = 2^x + 1, f(x) = 2x^2 + 1, f(x) = 2^(x+1), or something else? I’ll give the domain and range for the common possibilities:

- If f(x) = 2^x + 1:
- Domain: all real numbers (−∞, ∞).
- Range: (1, ∞) because 2^x > 0 for every x, so 2^x + 1 > 1 and approaches 1 as x → −∞.

- If f(x) = 2^(x+1):
- Domain: all real numbers (−∞, ∞).
- Range: (0, ∞) because exponential functions are always positive.

- If f(x) = 2x^2 + 1:
- Domain: all real numbers (−∞, ∞).
- Range: [1, ∞) because x^2 ≥ 0 so 2x^2 + 1 ≥ 1, with equality at x = 0.

- If f(x) = 4x + 1 (i.e., (2^2)x + 1):
- Domain: all real numbers (−∞, ∞).
- Range: all real numbers (−∞, ∞).

Tell me which one you meant and I’ll expand on the reasoning if you want.