Inverse of a Function Help?
f(x) = (4x-1) / (2x+3) Replace f(x) with y: y = (4x-1) / (2x+3). Switch x and y, then solve for y: x = (4y - 1) / (2y + 3) Clear denominator: x (2y + 3) = 4y - 1 Distribute: 2xy + 3x = 4y - 1 All y's on one side, everything else on the other: 2xy - 4y = -1 - 3x Factor out y: y (2x - 4) = -1 - 3x Divide by 2x - 4: y = (-1 - 3x) / (2x - 4) Rename y as f^(-1)(x) (f inverse of x): f^(-1)(x): = (-1 - 3x) / (2x - 4). Hope this helps.
Please help me solve this function I can not seem to figure it out!!?
The amount of garbage G produced by a city with a population p is given by G=f(p). G is measured in tons per week, and p is measured in thousands of people. a) the town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function f. b) Explain the meaning of the statement f(5)=2
Help!!! How do I solve this question??
I can t seem to figure out how to solve this question in my math assignment. Anyone able to walk me through the steps? "for the most visible star, delta cephei, the time between periods of maximum brightness is 5.4 days, the average brightness of the star is 4.0, and its brightness varies by +-0.35 magnitude. Find a function that models the brightness of delta cephei as a function of time.
How would I figure out the graph of this function: (2x^3+4x^2-9) / (3-x^2)?
x-intercept, when y = 0, or 2x^3 + 4x^2 -9 = 0, or x = 1.19 y-intercept, when x = 0, y = -9/3 = -3 For asymptotes, express the equation in partial fractions: y =(2x^3 - 6x + 4x^2 - 12 + 6x + 9) / (3 - x^2) = -2x - 4 - (6x + 9) / (x^2 - 3) Obviously there are asymptotes when x^2 - 3 = 0, or x = +/- sqrt 3 These are the vertical asymptotes There are no horizontal asymptotes, as x does not tend to infinity for any finite value of y, except infinity itself. Now when x gets large, pretty large, the remaining fraction in the expanded expression tends to zero. So then y = - 2x - 4 is the slant asymptote, with -2 gradient and -4 intercept So the graph goes like this: i. it starts from (-sqrt 3, -infinity), comes up, crosses y-axis at (0,-3), crosses x-axis at (1.19,0), and proceeds to (sqrt3, infinity) ii. a hyperbolic portion between the asymptotes x = -sqrt3 and y = -2x-4, in the 2nd quadrant. iii. a hyperbolic portion between the asymptotes x = sqrt3 and y = -2x-4 in the 4th quadrant. Happy drawing. ..
Need help in Excel VBA creating custom functions.?
Your troubles are over. From the Excel menu bar, click Tools/Macro/Visual Basic Editor. In the VB Editor, clikc Insert/Module, and you'll get Module1. At the top you'll see Option Explicit. Skip a line (blank) and type the following: Public Function SalesTax(sglCost As Single) As Single SalesTax = sglCost * 0.075 End Function Go back to the worksheets. Type "10" (without the quote marks) in a cell. In the cell next to it, type "=SalesTax(A1)" (without the quote marks). You should get 0.75. That's the basics of how to do it. Tweak it to suit your needs.
How do I graph piecewise functions?
to graph this by hand, you draw up the x-y axes and then starting with the first condition, go to x=1 and from there on (as x increases, so to the right) draw the corresonding equation, in this case 2x. so that should be a sort-of steep line from the x-axis going up. then for the graph to the left side of x=1, draw a line for -x+3 that will end when it reaches x=1. this line should hit the y axis at y=3 and be a line with slope of -1. it will not reach the x axis (if i'm picturing it in my head properly) and so the gap between the two lines is ok. put a hollow dot at x=1 on the end of the line -x+3. if that was confusing just let me know
Python Stub Functions: Statistics?
I am having difficulty trying to figure out what python is asking me to define. I've tried multiple codes and I can not seem to get any help. Can anyone give me a hand? Define stubs for the functions called by the program. Each stub should print "FIXME: Finish function_name()" followed by a newline, and should return -1. Example output: FIXME: Finish get_user_num() FIXME: Finish get_user_num() FIXME: Finish compute_avg() Avg: -1 Code Given: " '''Your solution goes here''' user_num1 = 0 user_num2 = 0 avg_result = 0 user_num1 = get_user_num() user_num2 = get_user_num() avg_result = compute_avg(user_num1, user_num2) print('Avg:', avg_result)"