Question

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

• A. x=-2
• B. x=1
• C. x=2
• D. x=-1

Answer 1

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
$\Rightarrow$ 6x = 12
$\Rightarrow$ x = 2