SOLUTION: g={(2,-1),(0,9),(1,-6),(2,-2)} h(x)=2x+9 Find the following. g^-1(-2)= h^-1(x)= (h∘h^-1)(7)=

Algebra ->  Rational-functions -> SOLUTION: g={(2,-1),(0,9),(1,-6),(2,-2)} h(x)=2x+9 Find the following. g^-1(-2)= h^-1(x)= (h∘h^-1)(7)=      Log On


   

Question 1165125: g={(2,-1),(0,9),(1,-6),(2,-2)}
h(x)=2x+9
Find the following.
g^-1(-2)=
h^-1(x)=
(h∘h^-1)(7)=
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) g^-1(-2) is the x value that produces a y value of -2. From the given definition of g, that value is 2.

(2) h^-1(x)...

The formal algebraic approach: switch x and y and solve for the new y.

y+=+2x%2B9 --> x+=+2y%2B9

Solve for y:

2y+=+x-9
y+=+%28x-9%29%2F2

A simple way to find the inverse of a function for many relatively simple functions....

The function h(x) does this to the input: (1) multiply by 2; (2) add 9.

The inverse function has to "get you back where you started". To do that, it has to (1) subtract 9; (2) divide by 2.

So the inverse function is y+=+%28x-9%29%2F2

(3) By the definition of an inverse function, (h∘h^-1)(A)=A, so (h∘h^-1)(7)=7.