Thread: find the inverse

1. find the inverse

f(x) = e^(x^3) + 3x
show that f(x) is invertible

2. Hello,

$f'(x)>0$

Hence f is a strictly monotone function. And thus it is a bijection and is invertible.

3. thanks so much
can u help with this part as well

Let g(y) denote the inverse of f(x). What is the domain and range of g(y)? What is g(e+3)?
Find g'(e+3)

4. Originally Posted by rphagoo
thanks so much
can u help with this part as well

Let g(y) denote the inverse of f(x).

What is the domain and range of g(y)? the range and domain of f(x)

What is g(e+3)?

f(1) = e+3 , so g(e+3) = 1

Find g'(e+3)

$\textcolor{red}{g'(e+3) = \frac{1}{f'(1)}}$
...

5. thanks so much!