Elementary Functions practice questions

Question 1

For $f: \mathbb{R} 	o \mathbb{R}$, $f(x) = x^3$, the value of $f(-2)$ is:

Accepted Answer

$f(-2) = (-2)^3 = -8$.

Answer

$-8$

Answer

$-6$

Answer

$6$

Answer

$8$

Question 2

The maximal domain of $f(x) = \sqrt{x - 4}$ is:

Accepted Answer

$x - 4 \ge 0 \Leftrightarrow x \ge 4$. The domain is $[4, +\infty)$.

Answer

$\mathbb{R}$

Answer

$(-\infty, 4]$

Answer

$[4, +\infty)$

Answer

$(4, +\infty)$

Question 3

The solution of $\sqrt{x + 2} = 3$ is:

Accepted Answer

$x + 2 = 9 \Rightarrow x = 7$. Check: $\sqrt{9} = 3$ ✓.

Answer

$1$

Answer

$5$

Answer

$7$

Answer

$11$

Question 4

For $f(x) = 2^{x}$, the value of $f(3)$ is:

Accepted Answer

$f(3) = 2^{3} = 8$.

Answer

$6$

Answer

$9$

Answer

$8$

Answer

$5$

Question 5

The value of $\log_{2} 8$ is:

Accepted Answer

$2^{3} = 8$, so $\log_{2} 8 = 3$.

Answer

$4$

Answer

$2$

Answer

$3$

Answer

$1$

Question 6

For $f(x) = x^{3}$, the value of $f(-2)$ is:

Accepted Answer

$f(-2) = (-2)^{3} = -8$.

Answer

$-8$

Answer

$8$

Answer

$-6$

Answer

$6$

Question 7

The domain of $f(x) = \sqrt{x - 4}$ is:

Accepted Answer

Require $x - 4 \ge 0$, i.e. $x \ge 4$.

Domain: $[4, \infty)$.

Answer

$\mathbb{R}$

Answer

$[4, \infty)$

Answer

$(4, \infty)$

Answer

$(-\infty, 4]$

Question 8

Solve over $\mathbb{R}$ the equation $e^{2x} - 4e^{x} + 3 = 0$. The solution set is:

Accepted Answer

Set $X = e^{x}$, so $X $ $>$ $ 0$. The equation becomes
$$X^2 - 4X + 3 = 0$$
$$(X - 1)(X - 3) = 0$$
$$X = 1 \quad 	ext{or} \quad X = 3$$
Both roots are positive, so substitute back:
$$e^{x} = 1 \implies x = 0$$
$$e^{x} = 3 \implies x = \ln 3$$
The solution set is $\{0\,;\ \ln 3\}$.

Answer

$\{0\,;\ \ln 3\}$

Answer

$\{1\,;\ 3\}$

Answer

$\{\ln 3\}$

Answer

$\{1\,;\ \ln 3\}$

Question 9

For $x \in (0, 1)$, which inequality is correct?

Accepted Answer

For $x \in (0, 1)$, multiplying by $x$ shrinks the value: $x^3 = x \cdot x^2 < x^2$ since $0 < x < 1$.

Answer

$x^2 < x^3$

Answer

$x^3 < x^2$

Answer

$x^2 = x^3$

Answer

It depends on the specific value of $x$

Question 10

The value of $f(x) = x^{-2}$ at $x = 3$ is:

Accepted Answer

$f(3) = 3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9}$.

Answer

$-9$

Answer

$\dfrac{1}{9}$

Answer

$-6$

Answer

$9$

Elementary Functions

Problems & worked solutions

Problem 1 — Elementary Functions

Problem 2 — Elementary Functions

Problem 3 — Elementary Functions

Problem 4 — Exponential Function

Problem 5 — Logarithmic Function

Problem 6 — Power Function

Problem 7 — Radical Function

Problem 8 — Exponential Function

Problem 9 — Elementary Functions

Problem 10 — Elementary Functions

Which exam are you sitting?