Find the domain and range of the function.
Recall that the domain of any function is the set of all z7wT9K0n/siYxFLcjkZgzdyhR39iUiKQgaQmaJeE04dVMyc2/DWicQ==.
Because of the square root, real values of the function are restricted to be vljafyOhvFRb2cl8x7zWAf3oW8cIpGW6B61AEnHWW1ifKuVd6zt3zwgyD12RrF/HN2wsNcrWAeMr3tEj7hA8VllNcquvi1g26xjrnLOYgaLmN7z/i9fd2GUix5vlOV0T7/xR1w==.
Since $a - t can only be positive or zero, we have .
Solve this inequality for t.
nc1ItEz0kR4=
Thus, the domain D of function g in interval notation is ( ugHNTI1hRxM= , nc1ItEz0kR4= ] or in set notation D = {t: t ≤ nc1ItEz0kR4=}.
(Type "inf" for ∞ and type "-inf" for -∞)
The range of any function, f(x), is the set of all values of y for which there exists at least one x such that +HQLKRa8cTJvVXBo0FfhzIkd6R1BHTMOOVqWjc4cd5MBCkaYJ5gjkdQUia01cYPwN33bk2Gh2KWcd8NMXbO8GQ1m9qoGK/N/.
The only values a square root can produce are AWXjrcRpytWnSE3JwDODssGJj9lchLAeTzudD3x7GJ1KRYP0wFRs7w==.
Write this statement as an inequality for the given function g.
1Wh3cvJ2xF4=
Substituting values of the domain, t ≤ $a, into verifies the smallest value of the range is g(t) = 1Wh3cvJ2xF4=.
Thus, the range R of the function y=g(t) in interval notation is [ 1Wh3cvJ2xF4= , 3LecBr2w/JA= ) or in set notation R = {y: y ≥ 1Wh3cvJ2xF4=}.
(Type "inf" for ∞ and type "-inf" for -∞)