Evaluation and operations with functions
Consider f(x)=cubic root(x-1), find f(-26)
-3
Suppose H(x)=5x^7-6, find f(x) and g(x) such that (fog)(x)=H(x)
g(x)=x^7
f(x)=5x-6
Consider g(x)=(-x-4)/5, find g^(-1)(x)
g^(-1)(x)=-(5x+4)
Consider the function *view image*
Find:
f(-4)=
f(0)=
f(1)=
f(-4)=4
f(0)=1
f(1)=0
Consider r(x)=2x^2 and s(x)=3x, find
(r+s)(x)=
(r-s)(x)=
(r*s)(-1)=
(r+s)(x)=2x^2+3x
(r-s)(x)=2x^2-3x
(r*s)(-1)=6(-1)^3=-6
For the functions f(x)=3/(x+4) and g(x)=11/x, find the composition and the domain of (fog)(x).
(fog)(x)=3x/(4x+11) with domain
(-infinity,-11/4)U(-11/4,0)U(0,infinity)
Consider the function f(x)=sqrt(6x-30) for the domain [5,infinity).
Find the inverse and the domain of the inverse in interval notation.
f^{-1}(x)=x^2/6+5
Domain=[0,infinity)
Consider the function *view image*
Graph the function f.
*View image*
Consider g(x)=x+7 and f(x)=(x-4)(x-2),
a) Find (g/f)(-3)
b) Find all the values that are NOT in the domain of (g/f).
a) (g/f)(-3)=((-3)+7)/(((-3)-4)((-3)-2))=4/35
b) x=2,4
The volume V(r) in cubic meters of a spherical balloon with radius r (meters) is given by V(r)=4/3*pi*r^3.
The radius W(t) (meters) after t seconds is given by W(t)=7t+3.
Write a formula for the volume M(t) (in cubic meters) of the balloon after t seconds.
M(t)=4/3*pi*(7t+3)^3.
Consider the function f(x)=7x/(3x-4).
Find the inverse, the domain and the range of the inverse in interval notation.
f^{-1}(x)=-4x/(7-3x)
Domain=(-infinity, 7/3)U(7/3, infinity)
Range=(-infinity, 4/3)U(4/3, infinity)
Consider the function *view image*
Graph the function f. Is it continuous?
*View image*
No, it's not continuous.