If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Evaluate composite functions

You might need: Calculator


g(x)=3x2h(x)=9x\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.
Step 1g(7)=372=35Step 2h(7)=9(7)=63Step 3(gh)(7)=3563=1895\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?
Choose 1 answer: