Answer To: Microsoft Word - written assignments_MAT-231-GS-mar21 Copyright © 2021 by Thomas Edison State...
Gaurav answered on Jun 13 2021
Q.1 – Find the domain, range, and all zeros/intercepts, if any, of the function
h(x )= 3
x2+4
Sol. Domain of the function h(x) is all real numbers, i.e., x∈ℝ ; and the range of the
function is 0For finding zeros, h(x) must be equated to zero and then find the value of x, however for
given function there is no zeros.
For finding y-intercept, x will be equated to zero, then y-intercept will occur at (0, 0.75).
Q.2 – Find the domain, range, and all zeros/intercepts, if any, of the function
g(x)= 3
x−4
Sol. Domain of the function g(x) is all real numbers except x=4, i.e., (x∈ℝ : x≠4) ; and
the range of the function is (g∈ℝ: g≠0) .
For finding zeros, g(x) must be equated to zero and then find the value of x, however for
given function there is no zeros.
For finding y-intercept, x will be equated to zero, then y-intercept will occur at (0, -0.75).
Q.3 for the function
f (x)=x−8 , g(x )=5 x2
(a) determine the domain of the new function – (f+g)
Sol. New function will become,
f (x)+g(x)=5x2+x−8
and the domain will be all real numbers, i.e., (x∈ℝ)
(b) determine the domain of the new function – (f-g)
Sol. New function will become
f (x)−g(x )=−5 x2+x−8
and the domain will be all real numbers, i.e., (x∈ℝ)
(c) determine the domain of the new function – (f*g)
f (x)∗g (x)=5 x3−40 x2
Sol. Domain will be all real numbers, i.e., (x∈ℝ)
(d) determine the domain of the new function – (f-g)
f (x)/ g(x)=(x−8)
5 x2
Sol. Domain will be all real number except when x=0, i.e., (x∈ℝ : x≠0)
Q.4 A certain bacterium grows in culture in a circular region. The radius of the circle,
measured in centimetres, is given by
r (t)=6−[5/(t 2+1)]
where, t is time measured in hours since a circle of 1-cm radius of the bacterium was put
into the culture.
a) Express the area of the bacteria as a function of time
Sol. The area if bacteria (assume, A) will be equal to the area of circle; hence
A (t)=π∗r (t )2=π∗(6−[5/(t2+1)])2
A (t)=36π +(25π )/(1+t2)2−(60π )/(1+t 2)
b) Find the exact and approximate area of the bacterial culture in 3 hours.
Sol. Exact area of bacterial culture in 3 hours,
A (3)=30.25π
and the approximate area, A(3) = 95.03 sq.-cm.
c) Express the circumference of the bacteria as a function of time.
Sol. Circumference of the bacteria as a function of time, c(t), will be equal to the
circumference of...