Asked by Trish Goal
Define f(x)=3x-8. If f^-1 is the inverse of f, find the value (s) of x for which f(x)=f^-1(x). Thank you!
Answers
Answered by
Steve
f^-1(x) = (x+8)/3
So, we want
(x+8)/3 = 3x-8
x+8 = 9x-24
8x = 32
x = 4
3*4-8 = 4
(4+8)/3 = 4
Note that the same results could have been achieved by setting
f(x) = x
3x-8 = x
2x = 8
x = 4
Why? because f(f^-1) = x by definition.
So, if f^-1(x) = f(x), then
f^-1(f) = f^-1(x)
x = f^-1(x) = f(x)
So, we want
(x+8)/3 = 3x-8
x+8 = 9x-24
8x = 32
x = 4
3*4-8 = 4
(4+8)/3 = 4
Note that the same results could have been achieved by setting
f(x) = x
3x-8 = x
2x = 8
x = 4
Why? because f(f^-1) = x by definition.
So, if f^-1(x) = f(x), then
f^-1(f) = f^-1(x)
x = f^-1(x) = f(x)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.