Question

Find the domain and range.f(x) = x 2 + 51. Domain: All real numbers; range: y ≥ 52. Domain: x > 5; range: All real numbers3. Domain: All real numbers; range: y > 04. Domain: x > 0; range: All real numbers

Answer 1

f(x) is defined for all real numbers, therefore its domain is all real numbers.

Now, recall that a number squared is always greater than or equal to zero, therefore:

$x^2\ge0.$

The above inequality implies that:

$x^2+5\ge5.$

Answer: Domain: All real numbers; Range: y ≥ 5.