HenryN
08-14-2008, 01:57 PM
these questions were submitted by a student and answred by Kevin Armstrong, one of our senior instructors.
1) Which of the Following Functions f is f(x)=(x-1) for all x?
a) f(x)=1-x
b) f(x)=1-x(squared)
c) f(x)=x(squared)-(1-x)(squared)
d) f(x)=x(squared) * (1-x)(squared)
e) f(x)=x/1-x
the correct answer is (d) could you explain to what they are asking for and how do you solve this?
Kevins answer:
Note that for some functions f , f(x) = f(-x) for all numbers x
For example f(x) = x2 (f(x) = (-x)2 = x2 = f(x)
Here they want us to indentify the function for which f(x) = f(1-x)
The quickest approach in this case is to see whether f(0) = f(1) in each case.
Only f(x) = x2(1 – x)2 passes this test.
Also note that 1 – (1 – x) = x, so if
f(x)= x2(1 – x)2 , f(1 – x) = (1 – x)2x2 = f(x)
Question 2 from Official Guide 11th addition # 142 DS
if x is an interger, is 9 (to the x power) + 9 (to the negative x power) = b?
a) 3(to the x power) + 3(to the negative x power) = the square root of b +2
b) x is greater than 0 = b
the correct answer is (a), why is the answer not b?
Kevin's Answer:
Note that (2) only says that x >0. It says nothing about the value of b, so it can't be sufficient.
3rd Question from Official Guidebook, # 145
is 1/p greater than r/r(squared) + 2?
Kevin's Answer:
in (1) You correctly simplify the question to r + 2/r > r
You can square both sides and say that the square of the left side is greater than the square of the right only if you know that both quantities are positive:
Remember that if x < y < 0, x^2 > y^2 !
1) Which of the Following Functions f is f(x)=(x-1) for all x?
a) f(x)=1-x
b) f(x)=1-x(squared)
c) f(x)=x(squared)-(1-x)(squared)
d) f(x)=x(squared) * (1-x)(squared)
e) f(x)=x/1-x
the correct answer is (d) could you explain to what they are asking for and how do you solve this?
Kevins answer:
Note that for some functions f , f(x) = f(-x) for all numbers x
For example f(x) = x2 (f(x) = (-x)2 = x2 = f(x)
Here they want us to indentify the function for which f(x) = f(1-x)
The quickest approach in this case is to see whether f(0) = f(1) in each case.
Only f(x) = x2(1 – x)2 passes this test.
Also note that 1 – (1 – x) = x, so if
f(x)= x2(1 – x)2 , f(1 – x) = (1 – x)2x2 = f(x)
Question 2 from Official Guide 11th addition # 142 DS
if x is an interger, is 9 (to the x power) + 9 (to the negative x power) = b?
a) 3(to the x power) + 3(to the negative x power) = the square root of b +2
b) x is greater than 0 = b
the correct answer is (a), why is the answer not b?
Kevin's Answer:
Note that (2) only says that x >0. It says nothing about the value of b, so it can't be sufficient.
3rd Question from Official Guidebook, # 145
is 1/p greater than r/r(squared) + 2?
Kevin's Answer:
in (1) You correctly simplify the question to r + 2/r > r
You can square both sides and say that the square of the left side is greater than the square of the right only if you know that both quantities are positive:
Remember that if x < y < 0, x^2 > y^2 !