Question

f(x) = (5)/(sqrt(4-x)), g(x)=x+4

1. find domain of f

2. domain of g

3. (f∘g)(x)

4. domain (f∘g)

Answer #1

consider the funtion f(x)=3x-5/sqrt x^2+1. given
f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) Find the domain of f. (write in interval notation):
Df:=_____________?
b) Find the x- and y- intercepts. if any. (write your answers as
ordered pairs).
c) Find the asymptotes of f, if any. If there are not, write
why. (write answers as equations).
d) Find all of the critical numbers of f. on what intervals is f
increasing/decreasing?
show all work

What is the domain of the following functions?
(A) F(x)= x/sqrt (2x-4)
(B) F(x)= x-3/ sqrt(x^2-6x+9)

Find the domain of f(g(x)). f(x)= 5/x-1 g(x)=4/3x-2
If anyone can solve this and explain the steps I would greatly
appreciate it. I found an answer but I want to check if I did it
correctly.

Find domain and critical values of
A - f(x) = 4x - sqrt(x)
B - f(x) = ln(3-x^2)

Let f(x, y) = sqrt( x^2 − y − 4) ln(xy).
• Plot the domain of f(x, y) on the xy-plane.
• Find the equation for the tangent plane to the surface at the
point (4, 1/4 , 0).
Give full explanation of your work

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

If f(2) = 3, f'(2) = 5, g(2) = 1, and g'(2) = 4, find h'(x) and
r'(x) if h(x) = 2(f(x))3/2 and r(x) = g(x) + p g(x), and determine
the greater value between h'(2) and r'(2).

Find f o g and g o f
f(x)= 8/(x^2-1) , g(x) = x^3 +1
also find domain of f, g, f o g , and
g o f

Find the inverse function of f(x)= 1+2cos(x) and then find the
domain and the range of the function of both f and f^-1??
Find the inverse function of f(x)=sqrt(3-e^2x) and then find the
domain and the range of the function of both f and f^-1??

The domain of the function g(x) is -1<x<6 and
the range is -5<y<10.
Find the domain and range of the following given functions.
a). the domain of y=g(x-4) is?
b.) the range of y=g(x)+2 is?

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