Q7 of 41 Page 46

Let f, g : R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f - g and .

Given: f(x) = x + 1, g(x) = 2x – 3.

(f+g)x = f(x) + g(x)


= x+1+2x-3


⇒ (f+g)x = 3x-2


(f-g)x = f(x) - g(x)


= x+1-2x+3


⇒ (f+g)x = 4-x




More from this chapter

All 41 →
5

Find the domain and the range of the real function f defined by.

 6

Let be a function from R into R. Determine the range of f.

 8

Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

 9

Let R be a relation from N to N defined by R = {(a, b): a, b, εN and a = b2}. Are the following true?

(i) (a,a) ε R, for all a ε N


(ii) (a,b) ε R, implies (b,a) ε R


(iii) (a,b) ε R, (b,c) ε R implies (a,c) ε R.


Justify your answer in each case.