1.17 Homework: inverse functions

On our last “Sample Test,” we did a scenario where Sally distributed two candy bars to each student and five to the teacher. We found a function $c(s)$ that represented how many candy bars she distributed, as a function of the number of students in the room.

• a What was that function again?
• b How many candy bars would Sally distribute if there were 20 students in the room?
• c Find the inverse function.
• d Now—this is the key part—explain what that inverse function actually represents. Ask a word-problem question that I can answer by using the inverse function.

Make up a problem like #1. That is, make up a scenario, and show the function that represents that scenario. Then, give a word problem that is answered by the inverse function, and show the inverse function.

$y=2+\frac{1}{x}$

$\frac{\mathrm{2x}+3}{7}$

$2(x+3)$

$x^2$

$x^3$

(x ³ +10) ³

$y=\frac{\mathrm{2x}+1}{x}$

$y=\frac{x}{\mathrm{2x}\left[\right]1}$

“The functions $f(x)$ and $g(x)$ are inverse functions.” Express that sentence in math, instead of in words (or using as few words as possible).