EVALUATE THE INDICATED VALUE OF COMPOSITION FUNCTION FROM THE TABLE

Evaluate the indicated expression assuming that f, g, and h are the functions completely defined by the tables below :

(i)  (f o g) (1) 

(ii)  (f o g) (3)

(iii)  (g o f) (1)

(iv)  (g o f) (3) 

(v)  (f o f) (2)  

(vi) (f o g o h) (2)  

(vii)  (h o g o f) (2)

Solution :

(i)  (f o g) (1)

(f o g) (1) = f[g(1)]

= f(2)

= 1

(ii)  (f o g) (3)

(f o g) (3) = f[g(3)]

= f(1)

= 4

(iii)  (g o f) (1) 

(g o f) (1) = g[f(1)]

= g(4)

= 3

(iv)  (g o f) (3)

(g o f) (3) = g[f(3)]

= g(2)

= 1

(v)  (f o f) (2)

(f o f) (2) = f[f(2)]

=  f(1)

= 4

(vi) (f o g o h) (2)

(f o g o h) (2) = (f o g)[h(2)]

= (f o g) (3)

= f[g(3)]

= f(1)

= 4

(vii)  (h o g o f) (2)

(h o g o f) (2) = (h o g)[f(2)]

= (h o g) (1)

= h[g(1)]

= h(2)

= 3

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