f(x)= e^(3x)-k, where k is a constant that is greater than 0. what is f^-1(x)? what is the domain of f^-1(x) ?
- print Print
- list Cite
Expert Answers
hala718
| Certified Educator
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given that f(x) = e^(3x) - k
We need to find the inverse function f^-1 (x)
Let f(x) = y
==> y= e^(3x) - k
Now we will add k to both sides.
==? y+k = e^(3x)
Now we will apply the natural logarithm for both sides.
==> ln (y+k) = ln e^3x
==> ln (y+k) = 3x ln e
But ln e = 1
==> ln (y+k) = 3x
Now we will divide by 3.
==> x= ln(y+k) / 3
Now we will rewrite x as y.
==> y= ln (x+k) / 3
Then the inverse function is :
f^-1 (x) = (1/3) * ln (x+k)
Now we will find the domain.
We know that the domain is when (x+k) > 0
But we know that k> 0
Then the domain are x values such that x > -k
Then the domain is x E ( -k, inf)
Related Questions
- Which is the domain of the function f(x)=x/(3x-1)?
- 1 Educator Answer
- What is the range of f(x) = 1-3x if the domain is x>0?
- 1 Educator Answer
- f(x) = (x-3)/(x+1) find f'(0)f(x) = (x-3)/(x+1) find f'(0)
- 2 Educator Answers
- Let f(x)=sqrt(1-sinx)What is the domain of f(x), find f'(x), what is the domain of f'(x) and...
- 1 Educator Answer
- Given f(x) = k(2+x), find the value of k if f^-1 (-2) = -3
- 1 Educator Answer