Identify the function shown in this graph.
1 answer:
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Answer: 0
<u>Step-by-step explanation:</u>
g(x) = x² + 6x ; x ≥ -3
To find the inverse, swap the x's and y's and solve for "y":
x = y² + 6y
x + 9 = y² + 6y + 9 <em>add 9 to both sides to create a perfect square</em>
x + 9 = (y + 3)²
= y + 3 <em>take square root of both sides</em>
= y ; y ≥ -3
g⁻¹(0) =
=
= -3 ± 3
= -3 + 3 , -3 - 3
= 0 , -6
since the restriction is: y ≥ -3, then -6 is not valid
By the chain rule,
where .
We have component partial derivatives
Putting the appropriate pieces together and setting , we get