Daily Math · 2026-07-04

Question 1

For the hyperbola $\dfrac{x^2}{9} - \dfrac{y^2}{16} = 1$, the asymptotes have equations:

Accepted Answer

$a = 3$, $b = 4$, so asymptotes: $y = \pm \dfrac{4}{3}x$.

Answer

$y = \pm x$

Answer

$y = \pm 3x/4$

Answer

$y = \pm 4x/3$

Answer

$y = \pm 5x/3$

Question 2

Let $f: \mathbb{R} 	o \mathbb{R}$, $f(x) = 3x - 6$. The inverse $f^{-1}$ is:

Accepted Answer

$y = 3x - 6 \Rightarrow x = \dfrac{y + 6}{3}$, so $f^{-1}(y) = \dfrac{y + 6}{3}$.

Answer

$f^{-1}(y) = \dfrac{y}{3} + 6$

Answer

$f^{-1}(y) = \dfrac{y + 6}{3}$

Answer

$f^{-1}(y) = 3y + 6$

Answer

$f^{-1}(y) = \dfrac{y - 6}{3}$

Question 3

At a meeting, every pair of people shakes hands exactly once. If there are $45$ handshakes total, how many people are there?

Accepted Answer

$\dfrac{n(n-1)}{2} = 45 \Rightarrow n(n-1) = 90 \Rightarrow n = 10$.

Answer

$9$

Answer

$9.5$

Answer

$10$

Answer

$45$

Problems & worked solutions