Test: Functions- 3 - GMAT MCQ

In this case, we need to solve for the volume of the water tank, so we set the full volume of the water tank as x. According to the question, 4/7 -full  can be replaced as -full  would be 13/14x Therefore, we can write out the equation as: 

Then we can solve the equation and find the answer is 14 gallons.

Let's look at f,g,and h and see if any of them are functions.

1. f = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of X because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.

2. g = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of X because it contains no ordered pair with first coordinate 2.  Because the set X = {1, 2, 3, 4}, we need an ordered pair of the form (2,  ) .

3. h = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function.  Even though two of the ordered pairs have the same number (2) as the first coordinate, h is still a function of X because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.

This is a definition question.  The only choice that does not equal the others is f(y)=x².  This describes a function that assigns x² to some number y, instead of assigning x² to its own square root, x.

We are given f(x) and h, so the only missing piece is f(x + h).

f(x+h)=(x+h)²=x²+2xh+h²
Then

We look at the range of the function on each of the three parts of the domain. The overall range is the union of these three intervals.

On (−∞,−2), f(x) takes the values:

x<−2
2x−1<2(−2)−1
2x−1<−5
f(x)<−5
or (−∞,−5)

On [−2,2], f(x) takes the values:

−2≤x≤2
−3(−2)≥−3x≥−3(2)
6≥−3x≥−6
−6≤f(x)≤6,
or [−6,6]

On (2,∞), f(x) takes only value 5.
The range of f(x) is therefore (−∞,−5)∪[−6,6]∪{5} , which simplifies to (−∞,6].

Each term of the Fibonacci sequence is formed by adding the previous two terms. Therefore, do the same to form this sequence:

8+12=20

12+20=32

The easiest way to find the inverse of f(x) is to replace f(x) in the definition with y , switch y with x, and solve for y in the new equation.

y=5x−7
x=5y−7
x+7=5y−7+7
x+7=5y

The easiest way to find the inverse of f(x) is to replace f(x) in the definition with y , switch y with x, and solve for y in the new equation.

y=x³−8

x=y³−8

x+8=y³−8+8

x+8=y³

(f∘g)(x)=f(g(x))
=f(x²+4)
=(x²+4)²−4
=x⁴+8x²+16−4
=x⁴+8x²+12

Solve for A in this equation:
g(A)=5A−2=11
5A−2+2=11+2
5A=13
5A÷5=13÷5
A=2.6

4Θx=72
4x+100=72
4x+100−100=72−100
4x=−28
4x÷4=−28÷4
x=−7

This is equivalent to asking for the value of x for which f(x)=1, so we solve for x in the following equation:
f(x)=1
A(x−B)³=1

(5⊙5)⊙5 
=[(5−1)(5−1)]⊙5
=(4⋅4)⊙5
=16⊙5
=(16−1)(5−1)
=15⋅4=60

This can be seen as a sequence in which the Nth term is equal to N if N is not divisible by 3, and −N otherwise. Since 1,000 and 1,001 are not multiples of 3, but 1,002 is, the 1000th, 1001st, and 1002nd terms are, respectively,

1000,1001,−1002

and their sum is 

1000+1001+(−1002)=999

This can best be solved by rewriting √x as1/x² and using the power of a power property.
(f∘f)(x)=f(f(x)) =