Answer: 16. C 17. A 18. A
19 You got this! There is only one answer with the correct radius squared!
Step-by-step explanation:
For the coordinates of the center, flip the signs in the parentheses.
For the "=output": in the equation, square the given radius.
Center: (-14.4) the signs in (x + 14)²+(y - 4)² are the opposites.
Radius given: 2 Square it to get the =4
Given:
g(x) = (1/3)x + 2
Part (a)
To find the inverse:
Set y = g(x) = (1/3)x + 2
Swap x and y.
x = (1/3)y + 2.
Solve for y.
(1/3)y = x - 2
y = 3(x - 2).
Set g⁻¹(x) to y.
Answer: g⁻¹(x) = 3(x - 2)
Part (b)
Create the table shown below to graph g(x) and g⁻¹(x).
x g(x) g⁻¹(x)
---- --------- ---------
-8 - 2/3 - 30
-6 0 - 24
-4 2/3 - 18
-2 4/3 - 12
0 2 - 6
2 8/3 0
4 4/3 6
6 4 12
8 14/3 18
Note that when x = -6, g(x) = 0, so that (-6, 0) lies on he black liine.
Therefore the inverse function should yield (0, -6) to be correct. This is so, so g⁻¹ is correct.
Both g(x) and g⁻¹(x)satisfy the vertical line test, so both are functions.
Part (c)
Algebraically, we know that g⁻¹(x) is correct if g(g⁻¹(x)) = x
Use function composition to obtain
g(g⁻¹(x)) = (1/3)*(3x - 6) + 2
= x - 2 + 2
= x
Therefore g⁻¹(x) is correct.
This means that
+- 6 < √42 < +- 7
hope it helps
Answer:
wheres the image or text
Step-by-step explanation:
First, divide both sides by 3. I think your mistake was that you were multiplying -3. Please note that in order to cancel something out you need to do the reverse operation. The reverse operation of subtraction is addition and the reverse of multiplication is division.
3(a - 5) = -6
a - 5 = -2
Now add 5 to both sides
a - 5 = -2
+5 +5
a = 3
Hope this helps!
