TOPICS
This page:
functions
Search
Dr. Math
See also the
Internet Library:
functions
HIGH SCHOOL
About Math
Analysis
Algebra
basic algebra
equations/graphs/
translations
linear algebra
linear equations
polynomials
Calculus
Complex Numbers
Calculators/
Computers
Definitions
Discrete Math
permutations/
combinations
Exponents
Logarithms
Fibonacci Sequence/
Golden Ratio
Fractals
Functions
Geometry
Euclidean/plane
conic sections/
circles
constructions
coordinate plane
triangles/polygons
higherdimensional
polyhedra
nonEuclidean
practical geometry
symmetry/tessellations
History/Biography
Interest
Logic
Negative Numbers
Number Theory
Physics/Chemistry
Probability
Projects
Puzzles
Sequences/Series
Sets
Square/Cube Roots
Statistics
Transcendental
Numbers
Trigonometry

Browse High School Functions
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Composition of functions.
Domain and range.
Inverse of a function.
Piecewise functions.
 Inverse Functions: Arcsec(x) [02/11/1999]

If y = arcsec(x) then what does x equal? How is this problem related to
inverse functions?
 Inverse Functions in Real Life [01/25/2002]

I would like to know if you have a good example of how inverse functions
would be used in real life.
 Inverse Functions OneWay Only [06/01/1999]

Are there two functions, f and g, such that (f of g)(x) = x but (g of
f)(x) does not equal x?
 Inverse Functions  Which Statement is True? [09/20/1998]

Does (f o g)^(1) equal f^(1) o g^(1) or g^(1) o f^(1)? How can you
prove it?
 Inverse of a Function vs. Inverse Proportionality [11/20/2002]

Finding the inverse of a function and graphing yields a graph that has
been reflected in the line y = x relative to the function. Inverse
proportionality, however, yields a reciprocal relation graphically.
Why do these two things have similar names yet mean different things?
 Inverse of a Multivariate Function [05/30/2002]

Let f:NxN > N such that f(x,y) = 2^x(2y + 1)  1 for all natural
numbers x, y. Let the inverse of f, g be given by g:N > NxN. Find the
inverse of the function g.
 Inverse of arg(z) [10/10/2003]

What is the inverse of the function arg(z)?
 The Inverse of the Absolute Value Function [12/12/2008]

What is the inverse of the absolute value function? I know the range
must be restricted if the inverse is to be a function.
 Inverses [06/05/2001]

What is an inverse?
 Inverses and Reciprocals of Functions [09/28/2005]

What is the difference between f^(1)(x) and f(x)^(1)?
 Inverses of Trigonometric Functions [08/07/2002]

How can the functions cosine and sine have inverses of arcsin and
arccos respectively?
 Inverse Statements [08/20/1998]

Say there are 3 + 4 times as many girls as boys. Is this the same as
saying there are 3 + 1/4 as many boys as girls?
 Inverse Trigonometric Ratios [07/01/2003]

Why aren't the inverse trigonometric ratios equal to 1/(the ratio),
as is the case for numbers?
 Invertible Functions [06/06/2003]

Consider as a function from R > R (Real) and say whether the function
is invertible: h(x) = (sgn x)* sqrt(abs(x)) where sgn is +1 if x is
positive, 1 if x is negative, and 0 if x is 0.
 Inverting Functions [07/19/2002]

To find the inverse of a function y=f(x), do I interchange the
variables x and y, or do I solve for x in terms of y?
 Irregular Sinusoidal Curves [08/24/2004]

Can you create a sinusoidal function with a fixed period such that the
time span between the max and min is not the same as the time span
between the min and max?
 Is the Function Invertible? [09/22/1997]

For the following functions f(x) decide if the function is invertible as a
function from R to R...
 Is the Inverse a Function? [9/2/1996]

How do I find the inverses and determine whether the inverses are
functions?
 An Iterative Method of Calculating Pi [06/09/2004]

I recently saw a method of calculating pi that involves an iterative
function, P(n + 1) = P(n) + sin(P(n)) where P(n) is the approximation
of pi at the nth iteration.
 Linear Equations and Standard Form [04/04/2002]

What do the variables mean in the standard form of a linear equation
(ax+by=c)?
 Linearity and Concavity [12/07/2003]

Why does a linear function have no concavity?
 Line Crossing Horizontal and Vertical Asymptotes [03/16/1999]

For the function y = (5x+1)/(x^21), why does the line between its two
vertical asymptotes and one horizontal asymptote cross?
 Lipschitz Continuous Functions [04/27/2008]

Show that a Lipschitz continuous function is uniformly continuous on a
subset and that the converse is not necessarily true. Also, give an
example to show that Lipschitz continuous functions are not
necessarily differentiable.
 Logs of Complex Numbers [02/11/2004]

Give an example showing that Log(z1/z2) does not equal Log(z1) 
Log(z2) where z1 and z2 are complex numbers.
 Manipulating Roots [08/08/1998]

If a and b are the roots of the equation 3x^2  5x + 1 = 0, find the
equation whose roots are a/b and b/a.
 Max and Min of Functions without Derivative [04/22/2003]

Is there a general way to find the maximum and minimum of cubic
functions without using derivatives?
 Maximizing Output of a Restricted Function [11/1/1996]

Create a function whose domain is restricted to complex numbers but whose
range is real, that is, nonconstant, has no constant term, and contains
no number greater than 3.
 Measurable Functions [09/13/2004]

Can you provide some motivation for the definition of a measurable
function?
 Meromorphic Functions [09/18/1998]

What is a meromorphic function?
 The Meteorologists' Theorem [1/6/1995]

Prove the "Meteorologists' Theorem": At any given moment, there are two
diametrically opposite points on the (spherical?) Earth's surface where
the temperatures are equal and the barometric pressure are equal.
 Multiplying Square Roots of Negative Numbers [11/25/2003]

It seems to me there are two possible ways to interpret a problem like
sqrt(2) * sqrt(2). One way I get 2 and the other way I get 2.
Which solution is correct? What's wrong with the other one?
 Mystery Operation: What Do These Strange Symbols Mean? [03/09/2010]

How do you evaluate the composition of two functions when you don't
even recognize their operational symbols? Doctor Ian unravels the
mystery behind weird symbols, explains their instructional purpose, and
uses grouping parentheses to show how to compose functions according to
the order of operations.
 Naming and Graphing Functions [06/16/1997]

Can you tell me about the different families of functions?
 Natural Domain of a Function [03/12/1999]

Some inputs don't make sense for some functions.
 NewtonRaphson Method [02/28/2000]

How can I find the 1st, 2nd, 3rd iterations and the parameters of x^3 
13.1x^2 + 48.48x  46.62 using the NewtonRaphson method?
 NewtonRaphson Method [06/24/2009]

Are there any equations that cannot be solved using the NewtonRaphson
method, regardless of the initial estimate?
 Newton's Method for Finding Roots of Functions [06/03/2003]

Is there an easy way to learn and understand this method or an example
that would allow me to understand the steps taken to work through the
problem?
 Nondifferentiable Functions [11/6/1994]

In my calculus book, it mentions a function that is not differentiable
at any point due to the fact that it is not smooth at any point. It does
not go any farther, and I was interested in hearing more.
 Normalizing Ranges of Numbers [04/22/2002]

How do I convert ranges like 5200 to a scale of 110?
 O and o Functions [01/08/1999]

How do big O notation and little o notation show the relation between two
functions?
Page: [<prev]
1
2
3
4
5
6
7
[next>]
