Question:
Let f(x) = 4(x2+x), g(x)= √x+1, h(x) = g(f(x)). Find the domain and range of h(x).
Let f(x) = 4(x2+x), g(x)= √x+1, h(x) = g(f(x)). Find the domain and range of h(x).
Updated On: Jul 29, 2024
- (-∞, ∞) and (-∞, ∞)
- (0, ∞) and (-∞, ∞)
- (-∞, ∞) and (0, ∞)
- (0, ∞) and (0, ∞)
- None of these
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The Correct Option is C
Solution and Explanation
\(f(x) = 4(x^2+x)\)
\(h(x) = g(f(x)) = g(\sqrt{4(x^2+x)+1} = \sqrt{4x^2+4x+1}\)
= \(\sqrt{(2x+1)^2} = |2x+1|\)
So, the domain of \(h(x) \) is \((-∞, ∞)\).
The range of \(h(x) = (0, ∞)\) as the output will not contain any negative values.
Hence, option C is the correct answer.
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