Daily Math · 2026-06-25

Question 1

$\displaystyle\int 5 \, dx$ equals:

Accepted Answer

$\int c \, dx = cx + C$. So $\int 5 \, dx = 5x + C$.

Answer

$0$

Answer

$5$

Answer

$5x + C$

Answer

$\dfrac{x^2}{5} + C$

Question 2

Consider $f: \mathbb{R} 	o \mathbb{R}$, $f(x) = x^2$. Which statement is correct?

Accepted Answer

$f(-1) = 1 = f(1)$, so $f$ is not injective. The value $-1$ has no real preimage (since $x^2 \ge 0$), so $f$ is not surjective either.

Answer

$f$ is neither injective nor surjective

Answer

$f$ is injective but not surjective

Answer

$f$ is surjective but not injective

Answer

$f$ is bijective

Question 3

The set of all complex solutions of $z^2 = -4$ is:

Accepted Answer

$z^2 = -4 \Rightarrow z^2 + 4 = 0 \Rightarrow (z - 2i)(z + 2i) = 0$. Solutions: $z = 2i$ or $z = -2i$.

Answer

$\{2, -2\}$

Answer

$\{2i\}$

Answer

$\{2i, -2i\}$

Answer

$\{1 + i, -1 - i\}$

Problems & worked solutions