## 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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Mathematics
10 hours
2021-07-22T15:08:13+00:00
2021-07-22T15:08:13+00:00 1 Answers
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## Answers ( )

Answer:x = – , 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 = –

x – 2 = 0 ⇒ x = 2