Question

Let f(x) = 4(x2+x), g(x)= √x+1, h(x) = g(f(x)). Find the domain and range of h(x).

• A. (-∞, ∞) and (-∞, ∞)
• B. (0, ∞) and (-∞, ∞)
• C. (-∞, ∞) and (0, ∞)
• D. (0, ∞) and (0, ∞)
• E. None of these

Answer 1

The Correct Option is C

\(f(x) = 4(x^2+x)\)

\(h(x) = g(f(x)) = g(\sqrt{4(x^2+x)+1} = \sqrt{4x^2+4x+1}\)

= \(\sqrt{(2x+1)^2} = |2x+1|\)

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.