Help with function problem please.

[pancho]

For all real numbers v, the operation v* is defined by the equation v^*= v-(V/3). if (V^*)^*=8, then v=

15
18
21
24
27

Thanks!

[tishan]

I think it is 27...
(v-v/3)-(v-v/3)/3=8
2v/3-2v/9
v=27

[bluementor]

IMO B

[pancho]

B is the correct answer. Can someone please show me the steps involved.

Thanks much.

[philipja]

Here's how I did it

(V^*)^*=8

=> (v-(V/3))^* = 8 ---- statement 1

Let k = v-(V/3)

statement 1 can be re-written as

k^* = 8

=>k-(k/3) = 8
=> 3k - k = 24
=> 2k = 24
=> k =12
=> v-(V/3) =12

=> 3v - v = 36
=> 2v = 36
=> v = 18

[Scott@TargetTestPrep]

For all real numbers v, the operation v* is defined by the equation v^*= v-(V/3). if (V^*)^*=8, then v=

15
18
21
24
27

Thanks!

Solution:

We can let w = v*; thus, we have (v*)* = w* = 8. That is,

w - w/3 = 8

2w/3 = 8

w = 8 x 3/2 = 12

Now, we earlier defined w = v*, and since w = 12, we have w = v* = 12, or:

v - v/3 = 12

2v/3 = 12

v = 12 x 3/2 = 18

Answer: B