Answer:
0
(1/3)x+13/3
5
Step-by-step explanation:
1. Like any function, <em>g</em> takes numbers from it's domain (-8, -3, 0, 7), and transforms them into numbers in it's range (8, 6, -3, 3). <em>g</em>^-1, it's inverse, maps back from the range into the domain. Since <em>g</em> maps 0 onto -3, g^-1 must turn -3 back to 0
g(0)=-3 == g`(-3)=0
2. To find the inverse of <em>h</em>, let h(x)=y.
Now, <em>y</em><em>=</em><em>3</em><em>x</em><em>-</em><em>1</em><em>3</em>
Remember that the inverse maps from the range (the y values) back to the domain (the x's), We want the function that takes a <em>y</em> and turns it into an <em>x</em><em>.</em><em> </em>For this, we must solve for x.
From above, <em>y</em><em>/</em><em>3</em><em>+</em><em>1</em><em>3</em><em>/</em><em>3</em><em>=</em><em>x</em>
Now that we rearranged <em>h</em>, we must flip the x and y to get the inverse. This happens because the range of <em>h</em> acts as the domain for <em>h</em><em>^</em>-1
3. The function <em>h</em> will turn 5 to some unknown number. Let's call it w. Then, if you pass w to h^-1, it will be turned back to a 5.
This is equivalent to computing the functions in the reverse order, or writing the composite, which results in x=y, and then computing
at²
= t² 
= t