Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
17 Cards in this Set
- Front
- Back
|
Let f(r) and h(t) be functions with real world meanings.
What is the general sentence that describes the meaning of f(h(t))? |
The real world meaning is: (meaning of f) in terms of (meaning of t). in other words, the meaning of the outermost function with respect to the inner most input.
|
|
|
What is the meaning of k(g(t)) where L=k(h) is the length of a steel bar at temperature H and H=g(t) is the temp at time t?
|
meaning of k(g(t)) is the meaning of the outermost function in terms of the inner most input.....
Thus k(g(t)) gives the length of a steel bar in terms of the time. |
|
|
If you are given a table of values for f(x), g(x), h(x) and are told to fill in the blanks for
h(x)=g(f(x)), then what two functions do you assume have the same input values? |
h and f
|
|
|
What are the steps for finding an inverse function?
|
1. Take the original equation and solve for the input in terms of the output.
2. Replace the input with f inverse of whatever the question asks 3. Make sure your input for your inverse function matches the variables in the equation |
|
|
True or false: If there is a horizontal line which intersects a functions graph in more than one point, then the function is guaranteed an inverse
|
False. if the line intersects in more than one point, the function does not have an inverse.
|
|
|
If you are given a function whose graph fails the horizontal line test, how can you alter the function so that it passes the horizontal line test?
|
Restrict the functions domain so that the horizontal line only intersects the function at one point.
|
|
|
The graph of a function and its inverse are symmetric about ....
|
The line y=x. You can also call this being symmetric about the origin
|
|
|
If (a,b) is a point on the graph of a function, then what point do we know is on the graph of the inverse function?
|
(b,a)
|
|
|
If f(cookies)=milk then what is true of the inverse function?
|
finverse(milk)=cookies
|
|
|
Given the domain and range of a function f, what are the domain and range of its inverse?
|
domain=range of f
range=domain of f |
|
|
If you are given f and g, how can you algebraically prove that f is the inverse of g and vice versa?
|
show that f(finverse(x))=x
or finverse(f(x))=x |
|
|
If g and f are inverses then what is the value of g(f(5/(n^2)-200))?
|
5/(n^2)-200
|
|
|
True or false,
in general, f(g(x))=g(f(x)) |
false
|
|
|
If f(x)=x^2 and g(x)=sin(x), then what is f(g(x))?
|
(sin(x))^2
|
|
|
If f(x)=x^2 and g(x)=(x+3)^0.5
then what is the domain of f(g(x))? |
Since the numbers under the square root have to be positive, we need
x+3>=0 Thus x>=-3 f(x)=x^2 is not restricted at all since this function can make sense of any input. Thus the domain is only restricted by g(x) so the domain is all x>=-3 |
|
|
Do most quadratic functions have inverses?
|
No, quadratic functions have parabolas for their graphs so their graphs will not pass the horizontal line test (unless the domain is restricted)
|
|
|
If the formula for the area of a circle is A=(pi)(r)^2, where r=radius
and the formula for the circumference is C=(pi)d, where d=diameter, what is the composition of A(C(d)) and what is its meaning? |
A(C(d))= A((pi)d)=pi((pi)d)^2
A(C(d)) gives the area in terms of the diameter |
