# inverse function question

Hey, I'm having trouble fully understanding absolute value graphs and I've been asked find the largest value of a so that f^-1 exists for the function:
f: (-efinity,a) --> R where f(x)= logel2x-1l

*note: i have used 'l' to represent the straight line indicating the it is an absolute value...

I know the answer is a=1/2 but i have no clue how to get that answer... Any help would be much appreciated :)

1. 👍
2. 👎
3. 👁
1. There is no such thing as the log of a negative number or zero. Because of the absolute value in the definition of f(x), the only value of x for which f(x) is not defined is x = 1/2.

An inverse function of f(x) can be defined for all x, but there will be two values of f^-1(x) for each x , since two different x values, symmetric about a=1/2, give the same f(x)

I don't know what you mean by
f: (-efinity,a) --> R

1. 👍
2. 👎

## Similar Questions

1. ### Precalculus

Which of the following functions have graphs that reflect their respective parent functions over the x-axis? Select all that apply. a. g(x) = -2^x b. g(x) = (-2)^x c. g(x) = 4th root(-3x) d. g(x) = -1/3 4th root(x) e. g(x) = -

2. ### mathematics

If you are having trouble with Lesson 11: Data and Graphs Unit Test CE 2015 Math 6 A Unit 3: Data and Graphs. here are the A's

3. ### math

find the slope of the following graphs. x -1,0,1,2 y 4,2,1,-2 a.1 over 2 b.2 c.-2* d.- 1 over 2 find the slope of the following graphs. x -2,2 y 5,1 a.3 over 2 b.1 c.-1* d.- 3 over 2 find the slope of the following graphs. x 0,3 y

How do you do Absolute Value Functions with graphs?

1. ### math, help

For the following set, which number has the largest absolute value? 4,-1,12,-20,19,0 Possible Answer of choice: A)0 B)19 C)-20 D)-1 wouldn't it be postive 20 but its not within the choices. What is the absolute value of -20?

2. ### Calculus

4. Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed by the graphs of f(x) = 18 – x^2 and g(x) = 2x^2 – 9.

3. ### science

An H-R diagram? Answer Are Is a map of the position of the stars Graphs stars according to their size and distance List every known star Graphs a sample of stars according to surface temperature and absolute brightness Thank You

4. ### Math

Lesson 8: Misleading graphs and statistics! I'm having trouble with the questions.

1. ### math

For the following set, which number has the largest absolute value? 4, –1, 12, –20, 19, 0 answer -20 is this correct?

2. ### Calculus

The shaded regions R1 and R2, shown below, are enclosed by the graphs of f(x)= −x^2 and g(x)= −2^x. (gyazo.com/7bcf02392ff69e2a1280588308342e8e) Find the x- and y-coordinates of the three points of intersection of the graphs

3. ### pre-calculus 11

I am asked to solve the absolute value equation of |1/2x +1| =x+1 graphically. I can solve this algebraically and consider two cases for the absolute value one being positive and the other negative. I know this will be a straight

4. ### Calculus

Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =