Consider the function $$f \left( x \right) =\frac{ 1 }{ 3 }x + 2$$
Find the inverse of f(x) and name it g(x). Show and explain your work.
let f(x) = y to yield: y = (1/3)x + 2
interchanging x and y yields: x = (1/3)y + 2.

solving for y yields y = f^-1(x) = 3x – 6?

Question

Consider the function $$f \left( x \right) =\frac{ 1 }{ 3 }x + 2$$ 
	Find the inverse of f(x) and name it g(x). Show and explain your work.
let f(x) = y to yield:  y = (1/3)x + 2
interchanging x and y yields: x = (1/3)y + 2. 

solving for y yields y = f^-1(x) = 3x – 6?

jango_in_dtown · Answer

Let y=f(x)=x/3 +2 then x/3=y-2 implies x=3(y-2)
so g(x)=3(x-2), the inverse of f(x)
second part we have x=(1/3)y+2 implies (x-2)=y/3 implies y=3(x-2)=3x-6
Hence y = f^-1(x) = 3x – 6

anonymous · Answer

thanks! :)