Answer:
<h2>
Hence a = -1, b = 10</h2>
Step-by-step explanation:
Given h(x) = (x - 1)³ + 10, f(x) = x + a and g(x) = x³ + b so that h(x) = (gof)(x)
To get the value of a and b that will make the composite function true, we will first need to get the composite function (gof)(x).
(gof)(x) = g[f(x)]
g[f(x)] = g[ x + a]
To get g(x+a), we will replace the variable x in the function g(x) = x+b with x+a as shown;
g[x + a] = (x+a)³+b
Hence (gof)(x) = (x+a)+b
Equating h(x) = (gof)(x)
(x - 1)³ + 10 = (x+a)³+b
On comparing both sides of the equation;
(x - 1)³ = (x+a)³ and 10 = b
For (x - 1)³ = (x+a)³
Take cube root of both sides
∛ (x - 1)³ = ∛(x+a)³
x-1 = x+a
collect like terms
a = x-x-1
a = -1
Hence a = -1, b = 10
Answer:
positive infinity bc it is going up
Answer:
x = -1
Step-by-step explanation:
First, add x to both sides.
-2x-6-x+x=-x-4x-8+x
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Next, Refine it.
-2x - 6 = -4x - 8
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Now, add 6 to both sides.
-2x - 6 + 6 = -4x - 8 + 6
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Now we Simplify.
-2x = -4x - 2
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Add 4x to both sides.
-2x + 4x = -4x - 2 + 4x
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Simplify again.
2x = -2
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Divide both sides by 2.
2x/2 = -2/2
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And we're almost finish! Just need to simplify.
x = -1.
Equivalent ratios: 12:14 18:21 24:28