Find the Domain and Range f(x)=x^2+1

Problem

ƒ(x)=x2+1

Solution

1. Identify the type of function. The function ƒ(x)=x2+1 is a polynomial (specifically a quadratic function).

2. Determine the domain. Since there are no denominators containing variables and no square roots of negative values, the function is defined for all real numbers.

3. Analyze the range by looking at the vertex. The term x2 is always greater than or equal to 0 for any real x

4. Calculate the minimum value. Adding 1 to both sides of the inequality x2≥0 gives x2+1≥1

5. Conclude the range. The output values ƒ(x) start at 1 and increase to infinity.

Final Answer

Domain: *(−∞,∞), Range: *[1,∞)

Want more problems? Check here!