The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > The function f(x) is defined as where x is no...

Join the Discussion on the App

The function f(x) is defined as

where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a?

a)
I only
b)
II only
c)
III only
d)
I, II and III
e)
None of the above

Correct answer is option 'B'. Can you explain this answer?

FREE This question is part of

Test: Functions- 2

Attempt Test

Attempt this Test

Verified Answer

The function f(x) is defined as where x is not equal to -1. If a is no...

Given:

Function f(x) is defined as
To find: Which of the 3 expressions is/are true for all values of a?

Approach:
Since the three expressions contain f(a – 1), f(a) and f(1), we’ll first find the expressions for these 3 functions
Then, we’ll evaluate the given expressions one by one.
Working Out:
Finding the expressions for f(a – 1), f(a) and f(1)

Evaluating Expression I

f(a−1)=f(a)–f(1)

We will assume that f(a-1) = f(a) – f(1) is true and then see if it leads to a real value of a or not.

Equating the above expression with the expression for f(a-1):

For no real value of a can the square of a+1/2 be negative
Therefore, no real value of a satisfies the equation given in Expression I.
So, Expression I is not true.

Since Left hand side of Expression II has the same value as the right hand side, this expression will hold true for all values of a.

Evaluating Expression III

f(a−1)=f(a)∗f(1)

The value of the left hand side of Expression III = 1/a
The value of the right hand side of Expression III = 1/2(a+1)
Equating the 2 values, we get:

Thus, Expression III is true for only 1 value of a (-2) – not for other values.
- So, Expression III is not a must be true expression.

Getting to the answer
- Thus, we have seen that out of the 3 expressions, only Expression II is a must be true expression.

Looking at the answer choices, we see that the correct answer is Option B

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

The function f(n) is defined as the product of all integers from 1 to n, inclusive, and the function g(n) is defined as the product of all odd integers from 1 to n, inclusive, where n is a positive integer. If p is a prime factor of {f(150)/g(150)} + 1, then which of the following must be true?

View answer

If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?

View answer

When y = 5x is rounded to the nearest integer, the result is 15. Based on this, the value of x may NOT be equal to which of the following values?I. 2.9II. 2.95III. 3.1

View answer

The function f(m) is defined for all positive integers m as the product of m + 4, m + 5, and m + 6. If n is a positive integer, then f(n) must be divisible by which one of the following numbers?

View answer

For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+4. Is the value of the function f(x) an even number? x is a multiple of 3 x is a prime number

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Top Courses for GMAT

View all

The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.

Solutions for The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The function f(x) is defined as where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a? a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam