Function Math Problems - Practice with Solutions

A function f has the form $f (x) = A e^{k x}$ . Find f if it is known that f(0) = 80 and f(1) = 144.

grabrovi0u 2022-10-20

Let n be a non-negative integer and let
$f (x) = \sum_{k = 0}^{n} (\binom{n}{k}) \sin^{k} x \sec^{k - n} x .$
Prove that f(x) is periodic and find its amplitude.

duandaTed05 2022-10-20

Why is the plot of $(x^{2})^{1 / 2}$ not the same as the graph of x?

klastiesym 2022-10-19

Try to figure out a function $f (n)$ which takes the input n, where $n \in N$ , and outputs the sum $\sum_{i = 0}^{i = n} k^{j i}$ till the $n^{t h}$ value where $k \in R$ & $j \in N$ . For example $\sum_{i = 0}^{i = n} 3^{2 i}$

Evelyn Freeman 2022-10-18

How to prove $\frac{d}{d x} \sinh x = \cosh x$ when $\sinh$ and $\cosh$ are defined by an integral?

greed 2022-10-17

Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:

Number of years 1 2 3
Car 1 (value in dollars) 17,390 16,346.60 15,365.80
Car 2 (value in dollars) 17,500 16,500 15,500

Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

Part C: Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years? Explain your answer, and show the value of each car after nine years. (4 points)

Source StylesNormalFontSize

Number of years	1	2	3
Car 1 (value in dollars)	17,390	16,346.60	15,365.80
Car 2 (value in dollars)	17,500	16,500	15,500

princetonaqo3 2022-10-17

If f is a continuous function from $[- a, a]$ to $R$ where $a \in R$ with a>0 and if the definite integral from −a to a of f is equal to 0 (with respect to x), then does that mean f must be odd?
I am struggling to find a counter-example so I tried to see if I could prove this statement but got stuck.
Is the statement true?

Stephany Wilkins 2022-10-17

Find the inverse function of each of the following functions. Specify the domains of the inverse functions.
$(a) f (x) = \frac{1}{5 x + 8} (b) g (x) = 4 \sqrt{3} - x - 7 (c) h (x) = \frac{5}{x + 3}$

Paola Mayer 2022-10-16

Given the one-to-one function $r (x) = \frac{2}{x + 5}$ Write the inverse function in inverse function notation.

Jack Ingram 2022-10-16

Check if the Mean Value Theorem can be applied to $f (x) = 4 \arccos (x)$ on [-1,1]
If so, find all values c in(-1,1) guaranteed by the mean Value theorem. If the Mean Value theorem does not apply, then justify that conclusion

Kevin Charles 2022-10-16

Take $\ddot{x} = w - 2 x + x^{2}$ , where $w \geq 0$ . Show that the evolution of x conserves a form of the energy and identify the potential function, sketching the phase portrait for $w = 0$

Tyson Atkins 2022-10-15

Write a possible function for: x-intercept = 0, y-intercept = 0, points of discontinuity = 2, -2. And, determine the intervals of x such that f(x) < 0.

Alexander Lewis 2022-10-15

Prove that $f (\underset{x \to + \infty}{lim sup} x_{n})$ = $\underset{x \to + \infty}{lim sup} f (x_{n})$
The problem is divided into two questions:
$x_{n}$ is a real valued sequence.
Prove that $f (\underset{n \to + \infty}{lim sup} x_{n})$ = $\underset{n \to + \infty}{lim sup} f (x_{n})$ given that f is continuous and increasing.
What can we say when f is decreasing.

Lance Liu 2022-10-15

Express the function H in the forn $f \cdot g$ .
$H (x) = \sqrt{7 + \sqrt{x}}$

djo57bgfrqn 2022-10-15

Refer to the function r, p, and q. Find the function $(r \cdot q) (x)$ and write the domain in interval notation.
$r (x) = - 2 x p (x) = x^{2} - 7 x q (x) = \sqrt{7 - x}$

Aryanna Blake 2022-10-14

Show that $x + a - [x - b], a, b \in R^{+}$ , is a periodic function. Find its period.

wasangagac4 2022-10-14

if $f (x + 3) = 2 x^{2} - 3 x - 1$ find $f (x + 1)$

Rubi Garner 2022-10-13

Given $h (x) = \frac{8 - x}{3}$ find its inverse

rancuri5a 2022-10-09

State the domain and the vertical asymptote of the function.
$g (x) = \ln (7 - x)$

Genesis Gibbs 2022-10-09

Find a formula for the linear function whose data is given in the table below.
$\begin{array}{ll} Year, t & 0 & 4 & 8 \\ Value of a computer, V & 1900 & 1620 & 1340 \end{array}$

Dealing with function Math questions is never easy as these can be implemented virtually anywhere where Algebra is used. It means that starting with at least one function Math example from what has been provided below will help you. Of course, certain function Math problems will require more analysis and verbal explanations, yet these are also encountered as you look through the questions. Learn about the use of equations first! The functions Math problems are always based on the analytical part because the function Math equation always has only one answer for every unknown variable.

Algebra I

Functions in Algebra Examples