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Artemon [7]
2 years ago
5

Given function of f(x) = 2x - 1 and fg(x) = 10x + 3, find the function of g(x)​

Mathematics
1 answer:
denis-greek [22]2 years ago
7 0

Answer:

The function of g(x) = 5x + 2

Step-by-step explanation:

Let us use the composite function to solve the question

∵ f(x) = 2x - 1

∵ f(g(x)) = 10x + 3

→ f(g(x)) means substitute x in f(x) by g(x)

∴ f(g(x)) = 2[g(x)] - 1

→ Equate the two right sides of f(g(x))

∴ 2[g(x)] - 1 = 10x + 3

→ Add 1 to both sides

∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1

∴ 2[g(x)] = 10x + 4

→ Divide each term into both sides by 2

∵ \frac{2[g(x)]}{2} = \frac{10x}{2} + \frac{4}{2}

∴ g(x) = 5x + 2

∴ The function of g(x) = 5x + 2

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