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)=

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) (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.

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Solve for y:

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

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

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