Functions Questions Homework Help: 3, 4, 8, 9 & 10

  • Thread starter gangsta316
  • Start date
  • Tags
    Functions
In summary, Homework Equations involve solving equations in terms of a function of two variables and composing them together. For 3, I got the inverse of the equation and for 4 I was unable to find a single equation that matched the given graph. For 8, it wants all solutions, which I'm not sure how to do. For number 9, I managed to get the double angle formulas but I'm still lost on how to do sinA + sinB and cosA + cosB. For 10, I was able to put tan x in terms of t but I don't know how to do sinx and cosx.
  • #1
gangsta316
30
0

Homework Statement



http://tinyurl.com/ylor68h

I'm having trouble with questions 3, 4, 8, 9 & 10.

Homework Equations





The Attempt at a Solution



For 3 I got
(b-dx)/(cx-a)
as the inverse and

[itex] \frac{(x(bc-ad))}{(acx + bc + cdx + d^2)}[/itex]

as the composed function. The bc - ad is there but it's on top of the fraction rather than the bottom so it would not cause the inverse to be undefined.


For 4 I drew the graphs but I can't express f(x) as a single equation.

I got
f(x) = H(x)*a(x) + something
but I don't know what what something is.


Can we do number 8 without using a calculator to find the value of x? And what does it mean that it wants all solutions -- aren't there infinitely many? I've solved the quadratics but I don't know how to get values of x without using a calculator and I don't see what it means by all solutions.


For number 9 I managed to get the double angle formulas, but I have no idea how to get sinA + sinB and cosA + cosB.


For number 10 I managed to put tan x in terms of t but I can't do it for sinx and cosx. I think that I just need a push in the right direction for this one.



Thanks for any help.
 
Last edited:
Physics news on Phys.org
  • #2
You'd probably get a faster response by not bundling so many questions in one post.
gangsta316 said:

Homework Statement



http://tinyurl.com/ylor68h

I'm having trouble with questions 3, 4, 8, 9 & 10.

Homework Equations





The Attempt at a Solution



For 3 I got
(b-dx)/(cx-a)
as the inverse and
This is what I got for the inverse, also.
gangsta316 said:
[itex] \frac{(x(bc-ad))}{(acx + bc + cdx + d^2)}[/itex]
In the line above, the numerator is fine, but the denominator isn't. You should have a couple of terms that cancel.
gangsta316 said:
as the composed function. The bc - ad is there but it's on top of the fraction rather than the bottom so it would not cause the inverse to be undefined.


For 4 I drew the graphs but I can't express f(x) as a single equation.

I got
f(x) = H(x)*a(x) + something
but I don't know what what something is.
What does the graph of y = H(-x) look like? Think of it as a reflection across one of the axes.
gangsta316 said:
Can we do number 8 without using a calculator to find the value of x? And what does it mean that it wants all solutions -- aren't there infinitely many? I've solved the quadratics but I don't know how to get values of x without using a calculator and I don't see what it means by all solutions.
For 8a, presumably you've already turned the equation into a quadratic-in-form in cosx. The equation you get can be factored, so you'll have one equation with cosx = some number, and another equation cosx = another number. One equation can be solved without a calculator, but the other one can't, so you have to write x as cos-1(something).

These equations give you one or two solutions in the interval [0, 2pi]. For all solutions (and, yes, there are an infinite number) you'll need to add integer multiples of 2pi.

I think 8b can be solved in a similar manner.
gangsta316 said:
For number 9 I managed to get the double angle formulas, but I have no idea how to get sinA + sinB and cosA + cosB.
For 9, nothing comes immediately to mind. You might try posting it in a separate thread.
gangsta316 said:
For number 10 I managed to put tan x in terms of t but I can't do it for sinx and cosx. I think that I just need a push in the right direction for this one.
Draw a right triangle with base 2 and altitude x, with angle t opposite the side of length x. Then t = tan(x/2), so x/2 = tan-1(t), or x = 2tan-1(t).

Now calculate sin(x) and cos(x) using the relationship between t and x in the triangle you drew. You'll also need the double angle formulas for sine and cosine.
gangsta316 said:
Thanks for any help.
 
  • #3
Thank you. I will try those things. Drawing a triangle for the last one seems like a good idea.

Mark44 said:
What does the graph of y = H(-x) look like? Think of it as a reflection across one of the axes.

I thought of that but are we allowed to use H(-x)? The question says that it should be in terms of a(x), b(x) and H(x).
Mark44 said:
Draw a right triangle with base 2 and altitude x, with angle t opposite the side of length x. Then t = tan(x/2), so x/2 = tan-1(t), or x = 2tan-1(t).

Now calculate sin(x) and cos(x) using the relationship between t and x in the triangle you drew. You'll also need the double angle formulas for sine and cosine.

Doing that, won't you get tan t = x/2 hence t = arctan (x/2)? I managed to get the right answer anyway, thanks to your hint of drawing a right triangle. It has base 1, height t and angle x/2 opposite the side with length t.
 
Last edited:
  • #4
gangsta316 said:
Thank you. I will try those things. Drawing a triangle for the last one seems like a good idea.



I thought of that but are we allowed to use H(-x)? The question says that it should be in terms of a(x), b(x) and H(x).
I'm pretty sure using H(-x) would be allowed. It's just the reflection of the graph of y = H(x) across the y-axis.
gangsta316 said:
Doing that, won't you get tan t = x/2 hence t = arctan (x/2)?
No, tan t = tan(tan(x/2)) != arctan(x/2)
The substitution was to let t = tan(x/2), so x/2 = tan-1(t), so x = 2tan-1(t).
gangsta316 said:
I managed to get the right answer anyway, thanks to your hint of drawing a right triangle. It has base 1, height t and angle x/2 opposite the side with length t.
 

FAQ: Functions Questions Homework Help: 3, 4, 8, 9 & 10

1. What are functions in programming?

Functions are blocks of code that perform a specific task and can be called multiple times within a program. They help to organize and reuse code, making it more efficient and easier to maintain.

2. Why are functions important in programming?

Functions help to break down complex tasks into smaller, more manageable parts, making it easier to write and understand code. They also promote code reusability, making it more efficient and reducing the chances of errors.

3. How do you define a function in programming?

A function is defined by using the keyword "function" followed by the function name, a set of parentheses, and a set of curly braces. Any necessary parameters are listed within the parentheses and the code to be executed is placed within the curly braces.

4. What is the difference between a function parameter and argument?

A function parameter is a variable listed in the function definition, while an argument is the actual value passed to the function when it is called. Parameters are used to define the function and arguments are used to supply the function with necessary values.

5. How do you call a function in a program?

To call a function, you simply use the function name followed by a set of parentheses. If the function has parameters, you would pass the necessary values as arguments within the parentheses. The function will then execute its code and return a result, if applicable.

Similar threads

Replies
3
Views
1K
Replies
5
Views
2K
Replies
6
Views
1K
Replies
2
Views
1K
Replies
11
Views
2K
Replies
3
Views
2K
Back
Top