Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
8.8k views
in Relations and Functions by (47.4k points)
closed by

If f(x) = x2, g(x) = 3x and h(x) = x – 2. Prove that (fog)oh = fo(goh).

1 Answer

+1 vote
by (47.8k points)
selected by
 
Best answer

f(x) = x2

g(x) = 3x

h(x) = x – 2

(fog)oh = x – 2

LHS = fo(goh)

fog = f(g(x)) = f(3x) = (3x)2 = 9x

(fog)oh = (fog) h(x) = (fog) (x – 2)

= 9(x – 2)2 = 9(x2 – 4x + 4)

= 9x2 – 36x + 36 … (1)

RHS = fo(goh)

(goh) = g(h(x)) = g(x – 2)

= 3(x – 2) = 3x – 6

fo(goh) = f(3x – 6) = (3x – 6)2

= 9x2 – 36x + 36 … (2)

(1) = (2)

LHS = RHS

(fog)oh = fo(goh) is proved.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...