posted by .

Mathmate, I really appreciate all your help regarding my composite function question below but I'm still in need of your help. I don't understand how the range of x^2-x+1 is R. Isn't this a parabola with a minimum for y? Also, I understand minimum and maximum values of sine but I don't know how to apply in my question. Again, many thanks for helping me out with this 'cause it's really bugging me.

  • Math -

    You're right. The range of an odd-degreed polynomial is ℝ but even degreed polynomials are limited on one side. It's a slip on my part.

    In this case, you need to find the minimum (at the vertex) of f(x)=x²-x+1 (1/2,3/4). So the range is [3/4,∞).

    To find the minimum and maximum values (range) of g(x)=sin²(x)-sin(x)+1,
    you would use differentiation to find the derivative, g'(x)=2sin(x)cos(x)-cos(x)
    and equate g'(x) to zero to get
    cos(x)=0 or sin(x)=1/2
    Solution set in [0,2π] is
    {π/2, 3π/2, π/6, and 5π/6}
    These are the possible locations for absolute minimum/maximum.
    Evaluate g(x) at these points and determine the values of the absolute minimum and maximum. These are the limits of the range, since g(x) is a continuous function.

    If you have not yet done differential calculus, you can draw the graph of g(x) and select points near which you can calculate a refined value of the absolute maximum and minimum.

    Here's graph of the function g(x) between 0 and 2π.

  • Math -

    Thanks very much for taking the time to help! Since I haven't done calculus, I'll try graphing.

  • Math -

    You're welcome!
    Post if you have other questions, or need more details.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    how to you find a composite function form of y in this problem?
  2. Algabra

    THe domain of the function y=X2+3 is the set of all real numbers. What is the range of the function?
  3. algebra 2

    A. I need to write an equation to the linear equation..(-2,-2), (3,3). B. I need to graph the function of y=|x| on a coordinate plane. C. I need to give one similarity and one differnce for the equations and graphs in parts A and B. …
  4. Math (Composite Functions)

    I don't understand this question at all. If f(x) = 4x - 3 and h(x) = 4x^2 - 21, find a function g such that f ͦ g = h.
  5. TO MathMate

    I just wanted to say thanks for all your help, I really do appreciate it :-)
  6. Math

    I have to find the domain and range for the composite of functions G(x)=sinx and h(x)=x^2-x+1. I'm confused about this and would really appreciate some help. Thanks.
  7. trigonometry (MathMate)

    MathMate i would really appreciate if you can show me where the logarithms can be used.I know they are unnecessary and I already found the answer without them but i still have to show my work using logarithms and they just confuse …
  8. Reiny!!!! math help

    We understand how to do the questions now and we are really glad n thankful, but the graphing portion of it is confusing. Continuation of the function. The teacher wants us to plot the points from the different parts of the questions …
  9. Algebra 2

    3. Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)2 – 3. (1 point) A- vertex: (2, –3); axis of symmetry: x = 2 B- vertex: (–2, –3); axis of symmetry: x = –2 C- vertex: (2, 3); axis of …
  10. Algebra

    Hiya! I have a function here: y = x^2 - 4x - 32 I have some questions about it. 1. I think this parabola opens up. Am I correct?

More Similar Questions