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In the xyplane, point of intersection of two functions f(x) = x2 and
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06 Sep 2023, 09:21
06 Sep 2023, 09:21
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Question Stats:
60% (01:24) correct
40% (01:39) wrong based on 5 sessions
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In the xy–plane, point of intersection of two functions \(f(x) = x^2\) and \(g(x) = x + 2\) lies in which of the following quadrants?
Indicate all that apply
A. I
B. II
C. III
D. IV
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Indicate all that apply
A. I
B. II
C. III
D. IV
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) ALL the GRE Quant and Verbal Practice Directories in ONE place (2023)
\(\Longrightarrow\) Best GRE Test Books of 2023
Re: In the xyplane, point of intersection of two functions f(x) = x2 and
[#permalink]
14 Sep 2023, 15:44
14 Sep 2023, 15:44
Expert Reply
OE
Given functions are 𝑓(𝑥) = 𝑥^2 and 𝑔(𝑥) = 𝑥 + 2
Let’s plot these two functions as 𝑦 = 𝑥^2 and 𝑦 = 𝑥 + 2, on the 𝑥𝑦-plane
As 𝑦 = 𝑥^2 and 𝑦 = 𝑥 + 2
On equating both the functions,
⇨ 𝑥^2 = 𝑥 + 2
⇨ 𝑥^2 − 𝑥 − 2 = 0
⇨ (𝑥 − 2)(𝑥 + 1) = 0
⇨ Hence, 𝑥 = 2 𝑜𝑟 𝑥 = −1
⇨ Accordingly, 𝑦 = 4 𝑜𝑟 𝑦 = 1
⇨ Hence, the two functions will intersect at two points, (2, 4) and (-1, 1).
⇨ So, the quadrants in which both the functions will lie are quadrants I and II
Ans. (A and B)
Given functions are 𝑓(𝑥) = 𝑥^2 and 𝑔(𝑥) = 𝑥 + 2
Let’s plot these two functions as 𝑦 = 𝑥^2 and 𝑦 = 𝑥 + 2, on the 𝑥𝑦-plane
As 𝑦 = 𝑥^2 and 𝑦 = 𝑥 + 2
On equating both the functions,
⇨ 𝑥^2 = 𝑥 + 2
⇨ 𝑥^2 − 𝑥 − 2 = 0
⇨ (𝑥 − 2)(𝑥 + 1) = 0
⇨ Hence, 𝑥 = 2 𝑜𝑟 𝑥 = −1
⇨ Accordingly, 𝑦 = 4 𝑜𝑟 𝑦 = 1
⇨ Hence, the two functions will intersect at two points, (2, 4) and (-1, 1).
⇨ So, the quadrants in which both the functions will lie are quadrants I and II
Ans. (A and B)
gmatclubot
Re: In the xyplane, point of intersection of two functions f(x) = x2 and [#permalink]
14 Sep 2023, 15:44
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