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)c(s) size 12{c \( s \) } {}that represented how many candy bars she distributed, as a function of the number of students in the room.

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 + 1 x y = 2 + 1 x size 12{y=2+ { {1} over {x} } } {}

2x + 3 7 2x + 3 7 size 12{ { {2x+3} over {7} } } {}

2 ( x + 3 ) 2 ( x + 3 ) size 12{2 \( x+3 \) } {}

x 2 x 2 size 12{x rSup { size 8{2} } } {}

x 3 x 3 size 12{x rSup { size 8{3} } } {}

(x³+10)³

y = 2x + 1 x y = 2x + 1 x size 12{y= { {2x+1} over {x} } } {}

y = x 2x 1 y = x 2x 1 size 12{y= { {x} over {2x left [ right ]1} } } {}

“The functions f(x)f(x) size 12{f \( x \) } {} and g(x)g(x) size 12{g \( x \) } {} are inverse functions.” Express that sentence in math, instead of in words (or using as few words as possible).