The functions g and h are given by g(x) = x + 1 and h(x) = x² Find the values of x for which hg(x) = 3x² + x – 5

Question

The functions g and h are given by g(x) = x + 1 and h(x) = x²
Find the values of x for which hg(x) = 3x² + x – 5

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Acacia 3 years 2021-07-22T15:08:13+00:00 1 Answers 48 views 0

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  1. Nem
    0
    2021-07-22T15:09:30+00:00
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    Answer:

    x = – \frac{3}{2} , x = 2

    Step-by-step explanation:

    To find h(g(x)) substitute x = g(x) into h(x) , that is

    h(g(x))

    = h(x + 1)

    = (x + 1)²

    = x² + 2x + 1

    For h(g(x)) = 3x² + x – 5 , then

    3x² + x – 5 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides

    2x² – x – 6 = 0 ← in standard form

    (2x + 3)(x – 2) = 0 ← in factored form

    Equate each factor to zero and solve for x

    2x + 3 = 0 ⇒ 2x = – 3 ⇒ x = – \frac{3}{2}

    x – 2 = 0 ⇒ x = 2

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