The domain of the function f(x) is open square bracket, minus, 15, comma, 8, close square bracket[−15,8] and the range is open square bracket, 4, comma, infinity, right bracket[4,∞). Using interval notation, find the domain and range of g, of, x, equals, minus, f, of, xg(x)=−f(x).
Question
The domain of the function f(x) is open square bracket, minus, 15, comma, 8, close square bracket[−15,8] and the range is open square bracket, 4, comma, infinity, right bracket[4,∞). Using interval notation, find the domain and range of g, of, x, equals, minus, f, of, xg(x)=−f(x).
Solution
The domain of the function g(x) remains the same as f(x) because changing the sign of the function does not affect the input values. So, the domain of g(x) is [-15,8].
However, the range of g(x) will be the opposite of f(x) because we are negating the function. This means we flip the output values across the x-axis. So, the range of g(x) will be (-∞, -4].
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