Functions

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!

  1. 👍 0
  2. 👎 0
  3. 👁 228
  1. 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)].

    1. 👍 0
    2. 👎 0
  2. write h(x) as composition of two functions h(x) = (fog)(x)

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

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    The weekly demand and supply functions for Sportsman 5 X 7 tents are given by the following respective functions where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity. Find the

  2. calculus

    Choose any two specific functions (not already chosen by a classmate) that have inverses. Use your chosen functions to answer any one of the following questions: If the inverses of two functions are both functions, will the

  3. Algebra

    Use composition of functions to show that the functions f(x) = 5x + 7 and g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.

  4. PreCalc

    Choose any two specific functions that have inverses. Use your chosen functions to answer any one of the following questions - If the inverses of two functions are both functions, will the inverse of the sum or difference of the

  1. Math

    Help me for this question on composite functions Does the composition of functions display the commutative property? Give an example of each case to illustrate your answer.

  2. Check my CALCULUS answers please!

    Any short explanation for things I got wrong would be great, too, if possible! Thanks in advanced! :) 8. Which of the following functions grows the fastest? ***b(t)=t^4-3t+9 f(t)=2^t-t^3 h(t)=5^t+t^5 c(t)=sqrt(t^2-5t) d(t)=(1.1)^t

  3. Math22

    1. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y= (g(x), f(u)) = 2. Write the composite function in the form f(g(x)). [Identify the inner function u =

  4. College Algebra! help!

    Consider the following functions f(x)= (7x+8)/(x+3) and g(x)= (3x-8)/(7-x) (a) Find g(g(x)) (b) Find g(f(x)) (c) Determine whether the functions f and g are inverses of each other.

  1. math

    consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverse of each other. I have no clue where to even begin!

  2. Trig

    The point (1/3,1/4) lies on the terminal side of an angle. Find the exact value of the six trig functions, and explain which functions are reciprocal functions to each other.

  3. math

    Choose any two specific functions (not already chosen by a classmate) that have inverses. Use your chosen functions to answer any one of the following questions: If the inverses of two functions are both functions, will the

  4. Math

    Find the domain of the composite function, hog H(x)=√x , g(x)=-x+3

You can view more similar questions or ask a new question.