Maths true/false...?

Question

1. f(x) = |x| - 3 is a one to one function.
True
False


2. For any base a, Loga 1 = 0.
True
False


3. Solve: Log3 x = 2 (ONLY PROVIDE THE FINAL ANSWER).


4. For any base a, Loga ak = a.
True
False

Answer 1

1. False. f(1) = f(-1), for example, so its not one-to-one.
(Just to clarify, as some people may not know: the definition of one-to-one is that f(x) = f(y) only when x=y. The definition mentioned below is actually the definition of a *function*, not a one-to-one function.)

2. True. a^0 = 1 (assuming we are only talking about legitimate bases).
3. x = 3^2 = 9.
4. Did you mean log (base a) of a^k = a? In that case, its false. log (base a) of a^k is k.

Answer 2

(1) true. One-to-One means that for each x, there is only one possible y value.
(2) true. as long as a is a positive number. when you say that the Log (base a) of a number, say y, is equal to x, or in your terms, Loga y = x, another way of looking at it (the definition of the Logarithm) is that a raised to the powr of x is equal to y, or a^^x = y. In your case, a^^0 = 1 is true for every positive number.
(3) 9 (see previous answer)
(4) False. Counterexample: Suppose a = 2 and k = 4. By the definition of Logarithms, Loga ak would be Log2 2*4, which is (get your calculator out) 3. BUT, if you assume your statement to be true, this cannot be, since you would have Log2 2*4 = 2.

There is another case for (4) though. If you have it copied wrong or just do not understand the "Mathese" or how to write things in math when you do not use symbols, then your question could ask "TRUE OR FALSE? For every numbers a and k, Log base a of a to the k power is equal to k.", or as you may put it, Loga a^k = k. This would be a true statement AS LONG AS a is positive.

Answer 3

it quite is real and that i'm presenting you with the finished info for it from between the internet sites on the internet that can assist you in know-how. In arithmetic, a sq. variety, on occasion called a perfect sq., is an integer that is written as a results of fact the sq. of another integer; in different words, it quite is the fabricated from some integer with itself. So, as an occasion, 9 is a sq. variety, as a results of fact it quite is written as 3 × 3. sq. numbers are non-unfavorable. yet differently of asserting that a (non-unfavorable) variety is a sq. variety, is that its sq. root is returned an integer. as an occasion, ?9 = 3, so 9 is a sq. variety. a good integer that has no perfect sq. divisors different than a million is named sq.-loose. the common notation for the formulation for the sq. of a variety n isn't the product n × n, however the equivalent exponentiation n2, oftentimes pronounced as "n squared". For a non-unfavorable integer n, the nth sq. variety is n2, with 02 = 0 being the zeroth sq.. the assumption of sq. could be prolonged to three different variety structures. If rational numbers are risk-free, then a sq. is the ratio of two sq. integers, and, conversely, the ratio of two sq. integers is a sq. (e.g., 4/9 = (2/3)2). beginning with a million, there are sq. numbers as much as and which incorporate m.

Answer 4

t
t
f
f

Answer 5

true
false
9
false