College Algebra

1. Find the domain of the composite function f o g. f(x)= 2/x-3; g(x)= 7/x

2. Solve the following exponential equation. Exact answers only. 2^1-9x = e^2x

  1. 👍
  2. 👎
  3. 👁
  1. f(g(x)) = 2/(g(x)-3) = 2/(7/x)-3) = 2x/(7-3x)

    domain would be all reals except x = 7/3, but we have to recall that g(x) is not defined for x=0.

    So the domain of fog is all reals except 0, 7/3

    2^(1-9x) = e^2x

    take log of both sides, recalling that ln(a^b) = b*lna:

    (1-9x)ln2 = 2x
    ln2 - 9 ln2 * x = 2x
    2x + 9 ln2*x = ln2
    x = ln2/(2+9 ln2)
    or, if you want to be sneaky,

    ln2/(ln(e^2) + ln(2^9))
    = ln2/ln(512e^2)
    = log512e^22

    1. 👍
    2. 👎
  2. 1.
    fog(x) = 2 /[(7/x) - 3]
    simplifying,
    2x/(7 - 3x)
    Domain: all real numbers except 3, 0 and 7/3

    2.
    2^(1-9x) = e^(2x)
    get ln of both sides:
    ln 2^(1-9x) = ln e^(2x)
    (1-9x)*(ln 2) = 2x
    (1-9x)/(2x) = 1/(ln 2)
    1/(2x) - 9/2 = 1/(ln 2)
    1/(2x) = 1/(ln 2) + 9/2
    2x = 1/[1/(ln 2) + 4.5]
    x = 1/[2(1/ln 2 + 4.5)]
    x = 1/[2/(ln 2) + 9]
    x = 1 / [2/(ln 2) + 9(ln 2) / (ln 2)]
    x = 1 / [2 + 9(ln 2)] / ln 2
    finally,
    x = (ln 2)/(2 + (9 ln 2))

    hope this helps~ :)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra plz help

    1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8}**** B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/

  2. Algebra

    1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8}**** B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/

  3. calcius

    Determine whether the relation represents a function. If it is a function, state the domain and range. {(-2, 1), (-1, -2), (0, -3), (1, -2), (3, 6)} a. function domain: {-2, -1, 0, 1, 3} range: {1, -2, -3, 6} b. function domain:

  4. Math

    The function f(x)=(x-5)^2+2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function. a. restricted domain: x>or=5; f^-1(x)=5-sqrt(x-2) b. restricted domain: x>or=5;

  1. math

    Find the rules for (f∘g)(x) and (g∘f)(x) and give the domain of each composite function. f(x) = x^2 g(x) = √(1-x) The Domain of (f∘g)(x) is : (f∘g)(x) = The Domain of (g∘f)(x) is : (g∘f)(x) =

  2. college algebra

    Let f(x) = 1/x − 2 and g(x) = 1/x − 3 . Determine the domain of the composite function. (Enter your answer using interval notation.) g compose f _____? & Find the composite function. (g compose f)(x) = _____?

  3. math111(3)

    The function f(x)=(x+6)^2 is not one-to-one. Choose the largest possible domain containing the number 0 so that f(x) restricted to this domain is one-to-one. The largest possible domain is [-6,infinity) If the restriction function

  4. Calculus

    Explain, using the theorems, why the function is continuous at every number in its domain. F(x)= 2x^2-x-3 / x^2 +9 A) F(x) is a polynomial, so it is continuous at every number in its domain. B) F(x) is a rational function, so it

  1. Math

    . The volume of a rectangular box is given by the expression V = (120 − 6w)w2, where w is measured in inches. a. What is a reasonable domain for the function in this situation? Express the domain as an inequality, in interval

  2. 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

  3. Calc AB

    Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f –1(x)is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more

  4. Algebra 1 - Help!?

    Two big questions that are driving me mad. 1) Given the following linear function sketch the graph of the function and find the domain and range. f(x) = 2/7x - 2 2) Given the following linear function sketch the graph of the

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