Let F(X) = 2x + 5 And G(X) = X2 + X. Describe (I) F + G (Ii) F

0CBSECommerce (English Medium) Class 11Question PapersQuestion PapersTextbook Solutions12733MCQ Online Mock TestsImportant SolutionsConcept Notes & Videos134Time TablesSyllabusLet 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. - Mathematics

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Question

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.

SolutionShow Solution

Given:f(x) = 2x + 5 and g(x) = x2 + xClearly, f (x) and g (x) assume real values for all x.Hence,domain (f) = R and domain (g) = R.

\[\therefore D\left( f \right) \cap D\left( g \right) = R\]

Now,(i) (f + g) : R → R is given by (f + g) (x) = f (x) + g (x) = 2x + 5 + x2 + x = x2 + 3x + 5. Hence, domain ( f + g) = R .(ii) (f - g) : R → R is given by (f - g) (x) = f (x) - g (x) = (2x + 5) - (x2 + x) = 5 + x -x2 Hence, domain ( f -g) = R.(iii) (fg) : R → R is given by (fg) (x) = f(x).g(x) = (2x + 5)(x2 + x) = 2x3 + 2x2 + 5x2 +5x = 2x3 + 7x2 + 5xHence, domain ( f.g) = R .(iv) Given: g(x) = x2 + xg(x) = 0 ⇒ x2 + x = 0 = x(x+ 1) = 0⇒ x = 0 or (x + 1) = 0⇒ x = 0 or x = - 1

Now ,

\[\frac{f}{g}: R - \left\{ - 1, 0 \right\} \to R \text{ is given by } \left( \frac{f}{g} \right)\left( x \right) = \frac{f\left( x \right)}{g\left( x \right)} = \frac{2x + 5}{x^2 + x}\]

Hence,

\[\text{ domain } \left( \frac{f}{g} \right) = R - \left\{ - 1, 0 \right\}\]

shaalaa.comCartesian Product of Sets Report Error Is there an error in this question or solution? Q 2Q 1.2Q 3Chapter 3: Functions - Exercise 3.4 [Page 38]

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RD Sharma Class 11 Mathematics TextbookChapter 3 FunctionsExercise 3.4 | Q 2 | Page 38

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