64=2⁶ so 64^2/3=(2⁶)^2/3=2^6*2/3=2⁴=16

x = (y – 2)^1/3 = -1 . Correct answer is E.

Functions, which are represented by different formulas on different subsets of its domain are called piecewise defined functions, so the correct answer is C. Definitions for the other concepts regarding to functions in the other options are as follows:

Constant function and identity function are the concepts related to types of functions. A function assigning each element from its domain a single element in its range is called a constant function.

Given A ? , a function defined on the set A and assigning every element of A to itself is called the identity function.

Given a function  if the image is equal to the range, i.e. f (A)=B the function f  is called surjective (onto).

If a function which is both one-to-one and onto is called a bijection.

The vertex of  is, (0, -25) because -b/2a=0/2 and y=0^2-25=-25. The answer is B.

(x – 2) ( x – 1) > 0 ; (x > 2 or x < 1) = R \ [1, 2] . pg. 63. Correct answer is E.

The exponents in a polynomial function must be natural numbers. However 1.5 is not a natural number. Therefore the function f(x)=2x^1.5+1 is not a polynomial.

The interval consisting of the elements of both [-3, 5) and [-2, 0) is [-2, 0). The answer is B.

Operations on sets are somewhat similar to operations of addition, multiplication and subtraction of numbers.

Let A and B be two sets.

The set of elements that are in either A or B or both is called the union of the sets A and B and is denoted by A ? B, i.e.,

A ? B = {x| x ? A or x ? B}

The set of all elements of the sets A and B is called the union of the sets A and B and is denoted by

 A ? B.

Union is the act of combining two sets together into a single set.

Example

A = {1, 3, 5, 8}, B = {1, 3, 7}. Then A ? B = {1, 3, 5, 7, 8}.

If an element appears in both sets then we only list it once in the new set.

Example

A = {x| x is a city in Turkey with population greater than 1 million}, B = {x| x is a city in Turkey with population less than 500 000}. Then A ? B ={x| x is a city in Turkey with population greater than 1 million or less than 500 000}. The set of elements A which are not in B is called the difference between A and B and is denoted by A \ B.

A \ B = {x| x ? A and x ? B}

Example

A = {3, 5, 8, 10}, B = {4, 5, 9}. Then A \ B = {3, 8, 10}.

Example

A = {0, 1, 2, 3, 4, …}, B = {1, 3, 5, 7, …}. Then A \ B = {0, 2, 4, 6, ...}.

Usually the sets that we deal with are subsets of some ambient set. Such a set is called a universal set and is denoted by U. In other words, U is the universal set if all the sets under examination are subsets of U. The difference U \ A is called the complement of A and is denoted by A^c . That is,

A^c = U \ A = {x| x ? U and x ? A}

Example

U = {1, 2, …, 10}, A = {9, 10}. Then U \ A = {1, 2, …, 8}.

The intersection of two sets A and B, written A ? B is the set consisting of the elements of both A and B. Thus, A ? B = {x| x ? A and x ? B}

Example A = {1, 2, 3, 5, 8}, B = {2, 3, 10, 11}. Then

A ? B = {2, 3}. x ? A ? B if and only if x ? A and x ? B.

Example

A = {x| x is a city in Turkey with population less than 1 million},

B = {x| x is a city in Turkey with population greater than 500 000}.

Then A ? B ={x| x is a city in Turkey with population between 500 000 and 1 million}.

As also understood from the information given,

If A = {1, 2, 3, 5, 8} and B = {2, 3, 10, 11}, the expressions in the options;

I “A ? B = {2, 3}”

III “A \ B = {1, 5, 8}”

IV “B \ A = {10, 11}” are correct, so the correct answer is D.

If an element appears in both sets then we only list it once in the new set, so the expression in the option II “A ? B = {1, 2, 2, 3, 3, 5, 8, 10, 11}” is not correct. It is written as;

A ? B = {1, 2, 3, 5, 8, 10, 11}.

Correct answer is B.

Since g cannot be zero, f / g is meaningful, and the answer can be calculated. 

The answer is, then, (-2+6) / ((-1)² +3) = 4 / 4 ) = 1

(gof)(x)=g(f(x)) then (gof)(7)=g(f(7)) by the way f(7)=1-7=-6 (gof)(7)=g(-6)=-6-2=-8

This function makes sense if its denominator is not zero, i.e. the condition of 2x - 10 ? 0 should be satisfied. Hence, if x ? 5, this condition is satisfied.  Therefore, the largest domain of the function is R \ {5}.   

x = [4, 5]. Correct answer is C.

x{-1, 1}. pg. 52. Correct answer is A.

Let the function P(t) denote the number of the cells at time t in this culture. 

P(t) = P₀e^kt

P(0)=P₀=150

P(1)=P₀e^k.1 › P(1)=150e^k =600 › e^k=5 then k=ln4 =2ln2

The equation is, P(t) = 150e^2ln2t

for t=4›P(4)=150e^2(ln2).4

=150.2⁸=38400.

f(x)=x³-x²+5x-12 if we put 5 instead of x then,

f(5)=5³-5²+25-12=125-25+25-12=113