Answer:
[-5, 4) ∪ (4, ∞)
Step-by-step explanation:
Given functions:


Composite function:
![\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =\dfrac{1}{\sqrt{x+5}-3} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%28f%5C%3Ao%5C%3Ag%29%28x%29%26%3Df%5Bg%28x%29%5D%5C%5C%20%26%20%3D%5Cdfrac%7B1%7D%7B%5Csqrt%7Bx%2B5%7D-3%7D%20%5Cend%7Baligned%7D)
Domain: input values (x-values)
For
to be defined:


Therefore,
and 
⇒ [-5, 4) ∪ (4, ∞)
<h3>
Answer: approximately 2076.56001909938
cubic cm</h3>
====================================================
Work Shown:
V1 = volume of cylinder
V2 = volume of cone on top
V3 = V1+V2 = volume of entire 3D solid figure
-----------
V1 = volume of cylinder
V1 = pi*r^2*h
V1 = pi*8.75^2*5.8
V1 = 1395.06348773471 which is approximate
----------
V2 = volume of cone
V2 = (1/3)*pi*r^2*h
V2 = (1/3)*pi*8.75^2*8.5
V2 = 681.49653136466 which is approximate
----------
V3 = V1+V2
V3 = 1395.06348773471+681.49653136466
V3 = 2076.56001909938
Answer is approximate
The units for the volume are in cubic cm.
Answer:

Step-by-step explanation:
Given:
The function 'g(x)' is given as:

Now, the function 'f(x)' is given as:

So, the function 'f(x)' is a transformation of 'g(x)'.
In order to find f(x), we replace 'x' by
in the 'g(x)' function equation. This gives,

Using the identity
, we get:

Hence the function f(x) is given as:

Perpendicular to the base.
Hope this helps!!!