Q4 of 99 Page 34

Let f : R → R be defined by


Find (i) f(2) (ii) f(4) (iii) f( - 1) (iv) f( - 3).


i)f(2)


Since f(x) = x2 - 2 , when x = 2


∴ f(2) = (2)2 - 2 = 4 - 2 = 2


∴f(2) = 2


ii)f(4)


Since f(x) = 3x - 1 , when x = 4


∴f(4) = (3×4) - 1 = 12 - 1 = 11


∴f(4) = 11


iii)f( - 1)


Since f(x) = x2 - 2 , when x = - 1


∴ f( - 1) = ( - 1)2 - 2 = 1 - 2 = - 1


∴f( - 1) = - 1


iv)f( - 3)


Since f(x) = 2x + 3 , when x = - 3


∴f( - 3) = 2×( - 3) + 3 = - 6 + 3 = - 3


∴f( - 3) = - 3


More from this chapter

All 99 →
2

Define each of the following:

(i) injective function


(ii) surjective function


(iii) bijective function


(iv) many - one function


(v) into function


Give an example of each type of functions.


 3

Give an example of a function which is

(i) one - one but not onto


(ii) one - one and onto


(iii) neither one - one nor onto


(iv) onto but not one - one.


 5

Show that the function f: R → R : f(x) = 1 + x2 is many - one into.

 6

Show that the function f : R → R : f(x) = x4 is many - one and into.