Find the inverse of each relation:

y = (0.5)^(x+2)
y = 3log base 2 (x-3) + 2

For the first one I got y=log base 0.5 (x+2)...but the answer in the back of the textbook says that it is not x+2, but x-2. Can someone tell me why it would end up being x-2 and help me with the second one too.

I agree with your first answer.

y = 3log base 2 (x-3) + 2
y-2 = log3 (x-3)^3
take the log3 of each side..

log3 (y-2)= (x-3)^3
take the cube root of each side
1/3 log3 ((y-2)) = x-3
x= 1/3 log3 ((y-2))+3 but 3 is log3 (27)
x= 1/3 log3( y-2) + log2 (27)
= 1/3 log3 (27*(y-3))

check that.

the answer is y = (log0.5x) - 2

be careful where the bracket is.

for the second, after you interchange the x and y variables you would have
x = 3log2(y-3) + 2
x-2 = log2(y-3)^3

(y-3)^3 = 2y-3
y+3 = [2y-3]^(1/3)
y = [2y-3]^(1/3) - 3

the exponent on 2 inside the square bracket in the last 3 lines should have been x-2 instead of y-3

I kept copy-and-pasting so I kept copying my own typo.

If y is the x+2 power of 0.5, then you are correct. By definition, y is the log-to-base 0.5 of x+2

But they are asking for the inverse. What function of y is x?

(x+2) log 0.5 = log y (to any base)
x = [log y/log(0.5)] -2 (to any base)
= log(base0.5)y - 2

Yea, I figured out the first one.
y = (0.5)^(x+2)
x = (0.5)^(y+2)
log(base 0.5)x = y+2
log(base 0.5)x-2 = y

For the second one, Reiny, you're right.

Thanks all for the help.

  1. 👍 0
  2. 👎 0
  3. 👁 272

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra2

    Does the relation in the table represent direct variation inverse variation or neither? If it is a direct or inverse variation, write an equation to represent the relation. (x,y) (5,2) (10,1) (15,2/3) (20,1/2)

    asked by Sally on October 17, 2016
  2. Functions - math

    The function f is such that f(x) = a^2x^2 - ax + 3b for x

    asked by Desperately seeking help on October 15, 2016
  3. Functions - math

    The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a

    asked by Desperately seeking help on December 10, 2016
  4. Trigonometry

    Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then

    asked by Veronica on March 24, 2011
  5. Algebra

    Myra uses an inverse variation function to model the data for the ordered pairs below. (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) Which statement best explains whether an inverse variation function is the best model for the data?

    asked by Melanie on July 7, 2014
  1. algebra

    Can someone help with inverse relations and functions? is relation t a function? Is the inverse t a function? chart looks like: x 0 2 4 6 y -10 -1 4 8 If someone could please explain this problem

    asked by lee on December 10, 2012
  2. Algebra 2

    what is the inverse of the given relation? y=3x+12 help explain the steps??

    asked by Jasmine on January 29, 2015
  3. math please help

    use an inverse trig function to write theta as a function of x (There is a right triangle drawn. The hypotenuse is 2. Theta is the angle between the base and the hypotenuse. The base/adjacent side of theta is labeled(x + 1) The

    asked by Sushmitha on March 30, 2011
  4. College Algebra

    Consider the following Matrix: A= [-2 0 1 -1 -2 1 1 -1 0 ] Choose the correct description of A. Find A−1 if it exists. Multiple Choice homework question: 1) A is Nonsingular; that is, it has an inverse. A^-1= 2) A is singular;

    asked by Moses on February 1, 2017
  5. Algebra II

    Express as a single logarithm with a coefficient of 1. Assume that the logarithms in the given problem have the same base. 4log a-3log b+5log c

    asked by Arielle on November 8, 2011
  6. Math

    Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer. x; 5,10,15,20 y; 2,1 ,2/3,1/2 Can

    asked by Olivia N J on March 1, 2017

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