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Evaluate composite functions

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Given:

\begin{aligned} g(x)&=\dfrac{3}{x-2}\\\\ h(x)&=9x \end{aligned}

Danielle tried to evaluate left parenthesis, g, circle, h, right parenthesis, left parenthesis, 7, right parenthesis, but she made a mistake. Here is her work.

\begin{array}{lrl} \text{Step 1}&g(7) &= \dfrac{3}{7-2}\\\\ &&=\dfrac{3}{5}\\\\ \text{Step 2}&h(7) &= 9(7)\\\\ &&= 63\\\\ \text{Step 3}&(g \circ h)(7) &=\dfrac{3}{5} \cdot 63\\\\ &&=\dfrac{189}{5} \end{array}

What is the mistake in Danielle's work?

(Choice A)
left parenthesis, g, circle, h, right parenthesis, left parenthesis, 7, right parenthesis, equals, g, left parenthesis, h, left parenthesis, 7, right parenthesis, right parenthesis, not g, left parenthesis, 7, right parenthesis, dot, h, left parenthesis, 7, right parenthesis.
(Choice B)
left parenthesis, g, circle, h, right parenthesis, left parenthesis, 7, right parenthesis, equals, h, left parenthesis, g, left parenthesis, 7, right parenthesis, right parenthesis, not g, left parenthesis, 7, right parenthesis, dot, h, left parenthesis, 7, right parenthesis.
(Choice C)
g, left parenthesis, 7, right parenthesis, equals, start fraction, 1, divided by, 3, end fraction, not start fraction, 3, divided by, 5, end fraction.

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Algebra (all content)

Course: Algebra (all content) > Unit 7

Evaluate composite functions

Algebra (all content)

Course: Algebra (all content) > Unit 7

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