+59 f(x) = 2x+1
g(x)= 3x-2
Find:
a) f-1(x), the inverse function
b) f(g(x)), a composition
c) g(f(x)), another composition
d) 2f(g(x)) = 3g(f(x))
+130071 a) Inverse of f
Get x by itself, "swap" x and y
y =2x + 1
y-1 =2x
(y -1) / 2 = x
(x - 1) / 2 = y = the inverse
b) f(g) we are putting g into f
f(g) = 2( 3x - 2) + 1 = 6x - 4 + 1 = 6x - 3
c) g(f).....just the other way around.....we put f into g
g(f) = 3( 2x + 1) - 2 = 6x + 3 - 2 = 6x + 1
d) 2f(g) =3g (f)
2 (6x - 3) = 3(6x + 1)
12x - 6 = 18x + 3
12x - 18x = 3 + 6
-6x = 9
x = 9/-6 = -3/2
