# functions

1. ### Find the F inverse of 6 for a combined function - Algebraically

Hello, I am stuck with this problem. I can see that the answer is "1" in the graphing calculator but not able to find it algebraically. Find F-1(6) for F(x)= ex-1+ 2lnx + 5x Any help will be appreciated.
2. ### Helpppppp piecewise function related!!

The picture below represents the graph of function f. Sketch the graph of the function g defined as follows: (in the picture)
3. ### Number of significant digits for arcsin answer?

I'm working on Law of Sines problems and the text seems wholly inconsistent in the way it rounds answers and when it rounds them. For example, for $sin(B)=0.3674$ it gives $B=21.6^\circ$ (Note 3 significant digits with one decimal) For $c=\dfrac{8}{sin(36^\circ)}(sin(122.4^\circ))$ it gives...
4. ### Thinking Question Help plz

Hi guys, so i need a plan to execute the steps and follow these criterias but i cant even get a head start. Any help would be much appreciated. Thanks guys! Two rational variable expressions are divided and the simplified expression must meet the following conditions: —The simplified...
5. ### Investigate f(2x - 1) = x + 4

I ran across this question and am not sure of the answer. Needless to say, I'm having trouble with conceptualizing all of the facets of functions. The question is: Investigate and understand f(2x - 1) = x + 4 I get two different possible answers - Let z = 2x - 1 x = (z + 1)/2; Evaluating...
6. ### Solve determining inverse functions

Determine wether f(x) = 3x + 8 and g(x) = x - 8 / 3 are inverse functions. For f(x) = 3x - 19, find the inverse f-¹(x). Minus sign is supposed to be uppercase..
7. ### Finding Area Function in Terms of Length

My math teacher has only gone over questions like these once in class and does not really explain clearly, so I’m struggling with the whole question. Here it is. “There is 1500ft of fencing that needs to be closed off at all sides. Find the area function in terms of length, dimensions, and...
8. ### Function combinations

Hi, I hope someone can help. I'm trying to develop the equation for the following word problem: This is a question from my pre-calculus course, where we are expected to use our knowledge of function combinations to derive an equation for this context. However, I'm finding it to be rather...
9. ### Composition function word problem

Hi, I hope someone can help. I'm trying to answer the following question: So to summarize the question, I'm suppose to develop a function which expresses this discount cost in terms of the number of people attending. According to the textbook, this function would be: The issue is, is...
10. ### Maximum value of combined function

Hi, I hope someone can help. I'm currently working on 10c: I know that the equation for the function is (25+x)(20,000-750x). In terms of finding the point of maximum revenue, I'm finding a hard time doing so. When I plot this on a graph, I get very large values. The answer according to the...
11. ### Combinations Function word problem

Hi, I hope someone can help me figure out why the range for this word problem: Note: knowing example 3 isn't necessary. I have already developed the right equation for this word problem, which is f(x) = 5000 - 25t - 1000cos((pi/6)t). I now just need to determine what the range is...
12. ### Characteristics of combined functions

Hi, I hope someone can help. I'm hoping that someone help me understand combined function characteristics with the following examples: 1. y=2^x-x^3 would this function not have a relative maximum at x = 0.59? Would it also have a minimum at x = 8.177? 2. y = sin(2pix) - 2sin(pix) my textbook...
13. ### Graphing exponential functions

Hi, I hope someone can help. I'm trying to calculate what the instantaneous rate of change would be at year 2 for the following table: I'm suppose to plot these points on a graphing calculator and then find the values of y (students per computer) that are close to year 2, then use these...
14. ### Simplifying exponential expression

Hi, So I have the exponential expression (16x^6)^(1/2). I got the solution 4x^2, which I thought was correct. However, according to my textbook, the solution is 4|x|^2. Do anyone know why this is so? I hope someone can help!
15. ### Polynomial f(x) such that f(x)f(1/x)=f(x)+f(1/x)

My teacher said that the polynomial function such that f(x)f\left(\frac{1}{x}\right)=f\left(x \right )+f\left(\frac{1}{x} \right ) exists and that must be of the form f(x)=1 \pm x^n. But he didnt give any proof. Can anyone help me with a proof that the function satisfying the above condition can...
16. ### Help with exponential generating function proof

Use exponential generating functions to prove that: P(n) = P(n-1) + n, with n >= 1 and P(0) = 1 will result in this equation: P(n) = (1/2)n2 + (1/2)n + 1 I know how to do this with generating functions, you just plug in n=1, n=2, n=3,.... P(1) will result in (1/2)(1)2 + (1/2)(1) +1 which is 2...