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3 years ago

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The revenue for a small business is modeled by the function R(x) = 5x where represents the number of items soldThe cost function

is C(x) = 10 + 2x What function represents the business's profit function P(x) = (R - C)(x) ?

1 answer:

MAVERICK [17]3 years ago

7 0

Answer:

$P(x) = 3x - 10$

Step-by-step explanation:

Given

$R(x) = 5x$

$C(x) = 10 + 2x$

Required

Determine $P(x) = (R - C)(x)$

In functions;

$(f - g)(x) = f(x) - g(x)$

So, we have:

$P(x) = (R - C)(x)$

$P(x) = R(x) - C(x)$

Substitute values for R(x) and C(x)

$P(x) = 5x - (10 + 2x)$

Open bracket

$P(x) = 5x - 10 - 2x$

Collect Like Terms

$P(x) = 5x - 2x- 10$

$P(x) = 3x - 10$

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For f(x) = 5x + 1

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Answer:

A. $f(7) = 5(7) + 1\\\\f(7) = 36$

B. $f^{-1}(x) = \frac{x - 1}{5}$

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Step-by-step explanation:

A. To solve the first part of the problem we must replace $x = 7$ in the function $f(x) = 5x + 1$

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B. In part B we must find the inverse function of $f(x) = 5x + 1$

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