Finding function range f(x)=1/(1 - e^-x)- 1/x (x>0) How to find the maximum value of the function with infinite approximation

Finding function range f(x)=1/(1 - e^-x)- 1/x (x>0) How to find the maximum value of the function with infinite approximation

When x approaches positive infinity,
limf(x)=1
When x tends to zero
limf(x)=0.5
So 0.5

Finding the range of function
How to find the range of | a + 1 | / √ (a ^ 2 + 1),

When (0 1) is increasing and (1 + infinity) is decreasing, the range of 1 + | 2A | / (a ^ 2 + 1) is 1 to 2, and the range of the original formula is 1 to root 2. I don't know if it's right

Find the range of function!
Find the range of the following functions
Y = X-1 + 2 under root sign
y=x

X-1 under the root indicates that X-1 should be greater than or equal to 0, so x is greater than or equal to 1