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Question

Find x if , gff(x) = fgg(x), given f (x) = 3x +1 and g(x) = x + 3


Your Answer
A
x=-2
Your Answer
B
x=1
Correct Answer
C
x=2
Your Answer
D
x=-1

Solution

The correct option is C x=2
Given f (x) = 3x +1 and g(x) = x + 3
gff(x) = g [f {f (x)}]
(This means “g of f of f of x”)
gff(x) = g [f {f (x)}]
          = g [ f (3x +1)]
          = g [ 3(3x +1)+1]
          = g (9x + 4)
          = [ (9x + 4) + 3]
          = 9x + 7
fgg(x) = f [g {g (x)}]
(This means “f of g of g of x”)
fgg(x) = f [g {g (x)}]
           = f [ g (x + 3)]
           = f [ (x + 3) + 3]
           = f (x + 6)
           = [ 3(x + 6) + 1 ]
           = 3x + 19
Given,   gff(x) = fgg(x)
we get 9x + 7 = 3x + 19
6x = 12
x = 2

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