Answer:
<h2>
![{g}^{ - 1} ( - 2) = \frac{9}{2}](https://tex.z-dn.net/?f=%7Bg%7D%5E%7B%20-%201%7D%20%28%20-%202%29%20%20%3D%20%20%5Cfrac%7B9%7D%7B2%7D%20)
</h2>
Step-by-step explanation:
To find g-¹( 2) we must first find g-¹(x)
To find g-¹(x) equate g(x) to y
That's
y = g(x)
We have
y = - 2x + 7
Now interchange the terms that's x becomes y and y becomes x
We have
x = - 2y + 7
Make y the subject in order to find g-¹(x)
Move 7 to the left side of the equation
- 2y = x - 7
Multiply both sides by - 1
We have
2y = 7 - x
Divide both sides by 2 to make y stand alone
That's
<h3>
![y = \frac{7 - x}{2}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B7%20-%20x%7D%7B2%7D%20)
</h3>
So we have
<h3>
![g ^{ - 1} (x) = \frac{7 - x}{2}](https://tex.z-dn.net/?f=g%20%5E%7B%20-%201%7D%20%28x%29%20%3D%20%20%5Cfrac%7B7%20-%20x%7D%7B2%7D%20)
</h3>
Now to find g-¹(- 2) substitute the value of x that's - 2 into the expression
We have
<h3>
![{g}^{ - 1} ( - 2) = \frac{7 - - 2}{2} \\ {g}^{ - 1} ( - 2) = \frac{7 + 2}{2}](https://tex.z-dn.net/?f=%20%7Bg%7D%5E%7B%20-%201%7D%20%28%20-%202%29%20%3D%20%20%5Cfrac%7B7%20-%20%20-%202%7D%7B2%7D%20%20%5C%5C%20%7Bg%7D%5E%7B%20-%201%7D%20%28%20-%202%29%20%20%3D%20%20%5Cfrac%7B7%20%2B%202%7D%7B2%7D%20%20)
</h3>
We have the final answer as
<h3>
![{g}^{ - 1} ( - 2) = \frac{9}{2}](https://tex.z-dn.net/?f=%7Bg%7D%5E%7B%20-%201%7D%20%28%20-%202%29%20%20%3D%20%20%5Cfrac%7B9%7D%7B2%7D%20)
</h3>
Hope this helps you
The answer is 8.
2^-3 is 0.125.
Then 0.125 is divided by 1, equals 8.
Where’s the graph? I need it to answer the question
The equation of the function is y = sec(2(x + π/6)) + 2
<h3>How to determine the equation of the function?</h3>
The graph that completes the question is added as an attachment
From the attached graph, we have the following parameters:
- Local maximum = 3
- Local minimum = 1
- Period = 2
- Phase shift = π/6
A secant function is represented as:
y = A sec(b(x + c)) + d
Where:
A = 0.5 * (max - min) = 0.5 * (3 - 1) = 1
b = Period = 2
c = Phase shift = π/6
d = 0.5 * (max + min) = 0.5 * (3 + 1) = 2
Substitute these values in y = A sec(b(x + c)) + d
y = 1 * sec(2(x + π/6)) + 2
Evaluate
y = sec(2(x + π/6)) + 2
Hence, the equation of the function is y = sec(2(x + π/6)) + 2
Read more about secant function at:
brainly.com/question/13276558
#SPJ1
Answer:
g(f(-1)) = 48
Step-by-step explanation:
given the following
f(x) = 5x² + 2
g(x) = x²-1
g(f(x)) = g(5x²+2)
Replace x with 5x² + 2 in g(x) as shown;
g(5x²+2) = (5x²+2))²- 1
g(f(x)) = (5x²+2))²- 1
g(f(-1)) = (5(-1)²+2))²- 1
g(f(-1)) = (5+2))²- 1
g(f(-1)) = (7)²- 1
g(f(-1)) = 49 - 1
g(f(-1)) = 48