Question 56
Dodó's calculator has a special key $\mathrm R$. If the display shows $x\ne2$, pressing $\mathrm R$ displays $(2x-3)/(x-2)$.
a. If Dodó enters $4$ and presses $\mathrm R$, what number appears?
b. Dodó entered a number and pressing $\mathrm R$ left it unchanged. Which numbers could he have entered?
c. Dodó noticed that entering $4$ and pressing $\mathrm R$ twice returns $4$, and similarly for $5$. Does this happen for every number other than $2$? Explain.
a. If Dodó enters $4$ and presses $\mathrm R$, what number appears?
b. Dodó entered a number and pressing $\mathrm R$ left it unchanged. Which numbers could he have entered?
c. Dodó noticed that entering $4$ and pressing $\mathrm R$ twice returns $4$, and similarly for $5$. Does this happen for every number other than $2$? Explain.