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
4.9k views
in Sets, Relations and Functions by (50.8k points)

Let f(x) = 2x + 5 and g(x) = x2 + x. Describe 

(i) f + g
(ii) f – g
(iii) fg
(iv) f/g
Find the domain in each case.

1 Answer

+1 vote
by (51.9k points)
selected by
 
Best answer

Given as

f(x) = 2x + 5 and g(x) = x2 + x

Here, both f(x) and g(x) are defined for all x ∈ R.

Therefore, domain of f = domain of g = R

(i) f + g

As we know, (f + g)(x) = f(x) + g(x)

(f + g)(x) = 2x + 5 + x2 + x

= x2 + 3x + 5

Now, (f + g)(x) is defined for all real numbers x.

∴ The domain of (f + g) is R

(ii) f – g

As we know, (f – g)(x) = f(x) – g(x)

(f – g)(x) = 2x + 5 – (x2 + x)

= 2x + 5 – x2 – x

= 5 + x – x2

(f – g)(x) is defined for all real numbers x.

∴ The domain of (f – g) is R

(iii) fg

As we know, (fg)(x) = f(x)g(x)

(fg)(x) = (2x + 5)(x2 + x)

= 2x(x2 + x) + 5(x2 + x)

= 2x3 + 2x2 + 5x2 + 5x

= 2x3 + 7x2 + 5x

(fg)(x) is defined for all real numbers x.

∴ The domain of fg is R

(iv) f/g

As we know, (f/g) (x) = f(x)/g(x) 

(f/g) (x) = (2x+5)/(x2+x)
Here, (f/g) (x) is defined for all real values of x, except for the case when x2 + x = 0.

x2 + x = 0

x(x + 1) = 0

x = 0 or x + 1 = 0

x = 0 or –1

When x = 0 or –1, (f/g) (x) will be undefined as the division result will be indeterminate.

Thus, the domain of f/g = R – {–1, 0}

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

...