2 MC Questions about Exponential and Log Funtions

1 If -1<1

Then a^2 must positive valve, therefore 0 < a^2
Also, as a^2 must no more than 1, as 1^2 = 1

Therefore, B is true.

2 put the value into the equation

If (1, -1), then -1 = Log 0-1 is incorrect as log 0 is infitive

If (1, 0), then 0=log 0-4 is incorrect as log 0 is infitive

If (2,-1), then -1= Log 1-1 (correct as log 1=0 )-then the left hand size is equal to right hand size

If (2, 0) then 0 = Log1-1 is incorrect as left hand size is 0 is no equal to right hand size -1

Therefore , answer is C

if -1<1, then a should be -0.9999999 to 0.9999999, the answer of the Q1 should be 0<1, B

for the graph y = log(x-1)-1, you can see the chosen answer, x value is 1 & 2, for x = 2, log (2-1) = log(1) = 0, if x = 1, log (1-1) = log (0) = undefined, so value of x in this question must be 2, then y = log(2-1) - 1 = 0-1 = -1, answer is C

1. I guess you mean "if -1<1", i.e. a has an absolute value smaller than 1.
As a is real, a^2 must be non-negative (i.e. 0 or positive). However, as "a=0" is withiin the range of -1 to 1, a^2 can be zero. When a = 0, a^2 = a = 0.
Therefore, if the question is really "if -1<1", then none of A, B, C are correct.
And so, the answer is D!

2. The point is on the curve if and only if the x-y values satisfy the equation. So, put the x-y pairs into the equation and see if the equation is satisfied.
When x = 1, y = log(1-1) -1 = log 0 - 1, no solution, as log 0 is undefined.
When x = 2, y = log(2-1) -1 = log 1 - 1 = 0 - 1 = -1.
So, the answer is C.

2007-01-16 22:37:12 補充：
1. 如果 -1

2007-01-16 22:44:37 補充：
我上面的答案顯示有問題. 怪碼應該是"... you mean -1＜a＜1 ..... as a=0 is...... is really -1＜a＜1..."回應你書本的答案:1. 如果 -1＜a＜1 而沒有說 a≠0, 那麼B 肯定錯!2. 除非題目打錯了, 否則 D 肯定是錯的!

第一條的確係似打錯0左

但係第二條0既答案好似應該係 C
when x = 2
Log(2-1) = Log(1) = 0
y = log(1) - 1 = -1