H(x)=1/3x+4 and j(x)=3x-12

Question

Use composition to determine whether each pair of functions are inverse.

 

Answer 1

Kyle's work is true & correct but he did not follow instructions. He should show that j(H(x)) = x, i.e., doing the composition!

 

j(H)x)) = 3[ ] - 12 and we put H(x)'s expression inside the empty [ ].

 

j(H)x)) = 3[1/3x+4 ] - 12

           = x + 12 - 12 = x.   This prove that the two stated functions are inverses of one another.

 

Answer 2

H(x) = (1/3)x+4, j(x) = 3x-12

 

They are inverses if and only if H(j(x)) = j(H(x)) = x

 

H(j(x)) = H(3x-12) = (1/3)(3x-12) + 4 = x-4+4 = x

 

j(H(x)) = j((1/3)x+4) = 3((1/3)x+4) - 12 = x + 12 - 12 = x

 

Since H(j(x) = j(H(x) = x, H(x) and j(x) are inverse functions.  

Answer 3

To see if two functions are inverses of each other, take one function, swap x and y and solve for y:

 

j(x) = 3x - 12

y = 3x - 12

x = 3y - 12

x + 12 = 3y

x/3 + 4 = y

 

When you solve for y, you get x/3 + 4, which is the first function, so they are inverses of each other.