Functions

posted by .

consider the functions g(x)=(4-x^2)^0.5 and h(x)=(x^2)-5.

find the composite functions hog(x) and goh(x), if they exist, and state the domain and range of the composite functions.

------------------------------

ok, i have figured out that hog(x)=-1-X^2, but in my answer booklet it says that the domain of this function is -2<&=x<&=2, and the range is -5<&=y<&=-1. can someone please explain how i can get this answer??thanks

and i have no idea why the function goh(x) does not exist. help please!

  • Functions -

    hog(x) means that you first perform the function g(x), and then enter the result of that function as x in the second function h(x).
    The function g(x) is a square root, meaning that whatever is under the square root sign has to be positive (you can't take the square root of a negative number).

    4-x^2 is only positive if -2 <= x <= 2, so this is the domain of g(x) and since x can take on any value in h(x), it's also the domain of hog(x).

    Now, for the range, we have to check when h(x) takes on its largest and smallest values. When we draw the graph of x²-5, we notice that it is a parabole. We can easily determine that for x=0, the parabole will reach its lowest point, and then starts to rise again. Since the maximum value for x is 2 or -2, we check that for 2 or -2 h(x) reaches the value -1 (being its largest value for -2 <=x <= 2).
    So the range of hog(x) is -5<=y<=-1.


    As for goh(x), it does exist. if we replace every x in g(x) by h(x), we get goh(x). Since 4-(x²-5)² is only positive for -sqrt(7) until -sqrt(3) and from sqrt(3) untill sqrt(7), this function only has values in those places.
    So the domain of goh(x) = [-sqrt(7),-sqrt(3)] U [sqrt(3),sqrt(7)].

  • Functions -

    write h(x) as composition of two functions h(x) = (fog)(x)

    h(x) = 3 square root 7 + 3 square root of x

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. composite functions

    f(x)=2x-4, g(x)=x squared + 5x What is F o G and Domain Okay, we are given f and g as functions of x. To compose a function means to use one function, g in this case, as the argument of the other, f in this case. Thus we want f o g …
  2. Functions

    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.
  3. Composite Functions

    Find the composite functions for the given functions. (6 marks) f(x) = 4x + 1 and g(x) = x2 f(x) = sin x and g(x) = x2 - x + 1 f(x) = 10x and g(x) = log x
  4. Calculus

    Find the sum and difference functions f + g and f – g for the functions given. f(x) = 2x + 6 and g(x) = 2x - 6 f(x) = x^2 - x and g(x) = -3x + 1 f(x) = 3x^3 - 4 and g(x) = -x^2 + 3 State the domain and range for the sum and difference …
  5. Calculus

    Math questions, please help me? :(? Find the composite functions f o g and g o f for the given functions. f(x) = 10^x and g(x) = log x State the domain and range for each: f(x) = 4x + 1 and g(x) = x^2 f(x) = sin x and g(x) = x^2 -
  6. algebra functions

    can someone help me with this and explain it to me step by step so i can try to solve the remaining problems i have I have no idea of what I am supposed to do For each problem, construct two composite functions, . Evaluate each composite …
  7. algebra functions

    construct two composite functions, Evaluate each composite function for x=2. i do not fully understand functions yet can someone explain and show me what to do step by step f(x)=x+1 g(x)=x-2
  8. algebra functions

    can someone please check my answer For each problem, construct two composite functions, . Evaluate each composite function for x=2 f(x)=3x g(x)=1/x f(g)*(x)=3x(1)/x x=2 3x(1)/x=6 g(f)*(x)=(3x)=2*3x=6 x=2 3*(2)=6*6=36
  9. algebra functions check my answer

    For each problem, construct two composite functions, . Evaluate each composite function for x=2 f(x)=3x g(x)=1/x f(g)*(x)=3x(1)/x x=2 3x(1)/x=6 g(f)*(x)=(3x)=2*3x=6 x=2 3*(2)=6*6=36
  10. functions

    For each problem, construct two composite functions, . Evaluate each composite function for x=2 ok i have not dealt with composite functions can I please get some help with this as I have 20 questions to do can someone show me step …

More Similar Questions