MATH PLEASE HELP! FUNCTION INVERSES

Consider the function f(x) = 1/3x +2
a. Find the inverse of f(x) and name it g(x). Show and explain your work.

I THOUGHT IT WAS THIS BUT I THINK I AM WRONGf(x)=1/3x+2 : x - 2 = 1/3x : 3x – 2 = x g^-1(x) = 3x - 2


b. Use function composition to show that f(x) and g(x) are inverses of each other.
f(g(x))=f(3x-2)
= -2(3x)
= ????


c. Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.

a)
f=1/3x+2
f-2=1/3x
3x=1/(f-2)
x=1/(3f-6)
g=1/(3X-6) This is the inverse of f(x)

b)
f(g)=1/3g+2= 1/[3*1/(3x-6)]+2= x-2 +2=x

f(g(x))=x

then g(x)=f^(-1)(x)

c)
Draw f=1/3x+2
and g=1/(3x-6)

You can use "online plot sites" for that.