There were 2000 applicants for enrollment to the freshman class at a small college in the year 2010. The number of applications has risen linearly by roughly 150 per year. The number of applications f ( x ) is given by f ( x ) = 2000 + 150 x , where x is the number of years since 2010. a. Determine if the function g ( x ) = x − 2000 150 is the inverse of f . b. Interpret the meaning of function g in the context of this problem.
There were 2000 applicants for enrollment to the freshman class at a small college in the year 2010. The number of applications has risen linearly by roughly 150 per year. The number of applications f ( x ) is given by f ( x ) = 2000 + 150 x , where x is the number of years since 2010. a. Determine if the function g ( x ) = x − 2000 150 is the inverse of f . b. Interpret the meaning of function g in the context of this problem.
Solution Summary: The author explains that the function g(x)=x-2000150 is the inverse of the one-to-one function.
There were 2000 applicants for enrollment to the freshman class at a small college in the year 2010. The number of applications has risen linearly by roughly 150 per year. The number of applications
f
(
x
)
is given by
f
(
x
)
=
2000
+
150
x
,
where
x
is the number of years since 2010.
a. Determine if the function
g
(
x
)
=
x
−
2000
150
is the inverse of f.
b. Interpret the meaning of function g in the context of this problem.
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ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0.
y Af
-2
1
2 4x
a. The function is increasing when
and
decreasing when
By forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1
if a=2 and b=1
1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2
2)Find a matrix C such that (B − 2C)-1=A
3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY