Let f(x) = 3x + 2 and g(x) = (1/3)x - (2/3). Find f(g(x)) and g(f(x)). What can we conclude about...?

Question

these functions?

Are the f(g(x)) and g(f(x)) the same? please show work...

Answer 1

To find f(g(x)), you put in the g(x) for every x in f:
g(x)=x/3-(2/3)
f(g(x))=3(x/3-(2/3))+2
=x-2+2
=x

The same idea applies for g(f(x)):
f(x)=3x+2
g(f(x))=(1/3)(3x+2)-(2/3)
=x+(2/3)-(2/3)
=x

Because both equal x, g is the inverse of f.

Answer 2

f(g(x)) = 3(g(x)) + 2 = 3[(x/3) - (2/3)] + 2 = x - 2 + 2 = x

g(f(x)) = (1/3)(3x+2) - (2/3) = x + 2/3 - 2/3 = x

g is the inverse of f (and vice versa, of course)

standard method to find inverse:
y = 3 x + 2
y - 2 = 3x
(y-2)/3 = x = (1/3)y - (2/3)
-----

Since f(x) = 3x + 2, then whatever you put in the place of x in the bracket after the x also takes the place of x after the 3.

f(A) = 3(A) + 2

f(0) = 3(0) + 2 = 2
f(orange) = 3(orange) + 2

f( g(x) ) = 3 g(x) + 2 = 3[ (1/3)x - (2/3) ] + 2

Answer 3

f(x)=3x+2
g(x)=(1/3)x-(2/3)
f(g(x))=f((1/3)x-(2/3))
=3[(1/3)x-(2/3)]+2
=x-2+2
=x
g(f(x))=g(3x+2)
=(1/3)(3x+2)-2/3
=x+2/3-2/3
=x
f(g(x))=g(f(x)). Yes, they are the same.

Answer 4

continued from answer by cidyah:

therefore f & g are inverse of each other.