COMPOSITION OF FUNCTIONS WORKSHEET

(1)  Using the functions f and g given below, find f o g and g o f . Check whether  f o g = g o f .

(i) f(x) = x - 6, g(x) = x              Solution

(ii) f(x) = 2/x, g(x) = 2x2 - 1              Solution

(iii) f(x) = (x + 6)/3,  g(x) = 3 - x        Solution

(iv) f(x) = 3 + x,  g(x) = x - 4          Solution

(v)  f(x) = 4x2 - 1, g(x) = 1 + x          Solution

(2)  Find the value of k, such that f o g = g o f

(i) f(x) = 3x + 2, g(x) = 6x - k       Solution

(ii) f(x) = 2x - k, g(x) = 4x + 5      Solution

(3) If f(x) = 2x - 1, g(x) = (x + 1)/2, show that

f o g = g o f = x              Solution

(4)  (i) If f(x) = x2 - 1, g(x) = x - 2 find a, if g o f (a) = 1. Solution

(ii) Find k, if f(k) = 2k - 1 and f o f(k) = 5.     Solution

(5)  Let A, B, C  N and a function f : A -> B be defined by f(x) = 2x + 1 and g : B -> C be defined by g(x) = x2 . Find the range of f o g and g o f.       Solution

(6)  Let f(x) = x2 - 1 . Find (i) f o f (ii) f o f o f      Solution

(7)  If f : R -> R and g : R -> R are defined by f(x) = x5 and g(x) = x4 then check if f, g are one-one and f o g is one-one?       Solution

(8)  Consider the functions f(x), g(x), h(x) as given below. Show that (f o g) o h = f o (g o h) in each case.

(i) f(x) = x - 1, g(x) = 3x + 1 and h(x) = x2       Solution

(ii) f (x) = x2, g(x) = 2x and h(x) = x + 4      Solution

(iii) f (x) = x - 4, g(x) = x2 and h(x) = 3x - 5      Solution

(9)  Let f = {(-1, 3),(0, -1),(2, -9)} be a linear function from Z into Z . Find f (x).      Solution

(10)  In electrical circuit theory, a circuit C(t) is called a linear circuit if it satisfies the superposition principle given by C(at1 + bt2) = aC(t1) + bC(t2), where a,b are constants. Show that the circuit C(t) = 3t is linear.  Solution

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