Question

HELP ASAP ALGEBRA 2 QUESTION PLEASE!!!

Consider the function f(x)=1/3 x+4.
Find the inverse of f(x) and name it g(x) . Show and explain your work.
Use function composition to show that and are inverses of each other.
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.

Answer 1

a)
f(x) is the same as y
y=1/3 x +4

to find inverse, swap and x and y:
x=1/3 y + 4
x-4= 1/3 y
(x-4) x 3 = y
3x -12= y
the inverse(g(x)), is: 3x-12

b) if f(x) and g(x) are inverses of each other, than (f о g)(x) will end up with just "x"

(f о g)(x)=x
(f о g)(x)= f(g(x))
(f о g)(x)= f(3x-12)
(f о g)(x)= 1/3(3x-12)+4
(f о g)(x)= (3x-12)/3 +4
(f о g)(x)= x-4+4
(f о g)(x)= x

c)
You will find that the graphs are mirror images of each other
the graph for f(x) is an oblique line that passes through the points(-12,4)
the graph for g(x) is an oblique line that passes through the points(4,-12)