Find x if gff(x)=fgg(x), given f(x)=3x+1 and g(x)=x+3
Answers
Answer:
To find the value of x
Given : f(x) = 3x+1 , g(x) = x+3
LHS :
ff(x) = f [ f (x) ]
= f [ 3x+1 ]
= 3 [ 3x + 1 ] +1
= 9x + 3 +1
ff(x) = 9x +4
gff(x) = g [ ff(x) ]
= g [ 9x +4 ]
= [9x+4 ] +3
gff(x) = 9x +7
RHS :
gg(x) = g [ g(x) ]
= g [ x+3 ]
= [x+3 ] +3
gg(x) = x +6
fgg(x) = f [gg(x) ]
= f [x +6 ]
= 3 [ x+6 ] +1
= 3x + 18 +1
fgg(x) = 3x +19
gff(x) = fgg(x)
9x+7 = 3x + 19
9x -3x = 19 -7
6x = 12
x = 12/ 6
x = 2