GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If f(x) = x - 1 and g(x) = x2 - 1, which of the following pairs of x-v
[#permalink]
06 Feb 2022, 06:15
06 Feb 2022, 06:15
Expert Reply
00:00
Question Stats:
94% (01:24) correct
5% (00:35) wrong based on 19 sessions
Hide Show timer Statistics
If \(f(x) = x - 1\) and \(g(x) = x^2 - 1\), which of the following pairs of x-values satisfy the equation \(g(f(x)) = 0\)?
(A) -2, 1
(B) -1, 0
(C) 0, 1
(D) 0, 2
(E) 1, 2
(A) -2, 1
(B) -1, 0
(C) 0, 1
(D) 0, 2
(E) 1, 2
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If f(x) = x - 1 and g(x) = x2 - 1, which of the following pairs of x-v
[#permalink]
06 Feb 2022, 06:56
06 Feb 2022, 06:56
1
Carcass wrote:
If \(f(x) = x - 1\) and \(g(x) = x^2 - 1\), which of the following pairs of x-values satisfy the equation \(g(f(x)) = 0\)?
(A) -2, 1
(B) -1, 0
(C) 0, 1
(D) 0, 2
(E) 1, 2
(A) -2, 1
(B) -1, 0
(C) 0, 1
(D) 0, 2
(E) 1, 2
Approach #1: Algebra
We want values of x such that \(g(f(x)) = 0\)
Let \(f(x) = k\)
So we want: \(g(f(x)) = g(k) = 0\)
Plug \(k\) into the function \(g\) to get: \(g(k) = k^2 - 1 = 0\)
Add \(1\) to both sides of the equation: \(k^2 = 1\)
So, EITHER \(k= 1\) OR \(k= -1\)
In other words, EITHER \(f(x) = 1\) OR \(f(x) = -1\)
Since \(f(x) = x - 1\), we now have two equations to solve:
If \(f(x) = 1\), then we have: \(x - 1 = 1\), which means \(x = 2\) is one possible solution.
If \(f(x) = -1\), then we have: \(x - 1 = -1\), which means \(x = 0\) is another possible solution.
Answer: D
Approach #2: Test values from the answer choices (this very well may be the faster approach)
Let's first see if \(x = 0\) is a solution.
\(f(0) = 0 - 1 = -1\).
So, \(g(f(0)) = g(-1) = (-1)^2 - 1 = 1 - 1 = 0\). WORKS.
Since \(x = 0\) is a solution, we can eliminate answer choices A and E, since they don't include \(x = 0\) as a solution
Now let's see if \(x = 1\) is a solution.
\(f(1) = 1 - 1 = 0\).
So, \(g(f(1)) = g(0) = (0)^2 - 1 = 0 - 1 = -1\). Doesn't work.
Since \(x = 1\) is NOT a solution, we can eliminate answer choice C, since it says \(x = 1\) is a solution
Now let's see if \(x = 2\) is a solution.
\(f(2) = 2 - 1 = 1\).
So, \(g(f(2)) = g(1) = (1)^2 - 1 = 1 - 1 =0\). WORKS.
Answer: D
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1115
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: If f(x) = x - 1 and g(x) = x2 - 1, which of the following pairs of x-v
[#permalink]
07 Aug 2022, 09:38
07 Aug 2022, 09:38
1
Given that \(f(x) = x - 1\) and \(g(x) = x^2 - 1\) and we need to find the value of x for which \(g(f(x)) = 0\)
To find the value of g(f(x) we will first substitute the value of f(x), we get
g(f(x)) = g(x-1)
Now, in order to find the value of g(x-1), we need to compare what is inside the bracket of g(x) and g(x-1)
=> We need to put x = x-1 in \(g(x) = x^2 - 1\) to get the value of g(x-1)
=> g(x-1) = \((x-1)^2 - 1\) = \(x^2\) - 2x + 1 - 1 = \(x^2\) - 2x = 0 (given)
=> x * (x-2) = 0
=>x = 0, 2
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
To find the value of g(f(x) we will first substitute the value of f(x), we get
g(f(x)) = g(x-1)
Now, in order to find the value of g(x-1), we need to compare what is inside the bracket of g(x) and g(x-1)
=> We need to put x = x-1 in \(g(x) = x^2 - 1\) to get the value of g(x-1)
=> g(x-1) = \((x-1)^2 - 1\) = \(x^2\) - 2x + 1 - 1 = \(x^2\) - 2x = 0 (given)
=> x * (x-2) = 0
=>x = 0, 2
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
