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Novosadov [1.4K]
4 years ago
14

Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type your answers in the box

Mathematics
1 answer:
anastassius [24]4 years ago
3 0
F(x) = (1/2)x + 4
Plug y in for f(x).
y = (1/2)x + 4
Swap x and y.
x = (1/2)y + 4
Solve the equation for y =.
Subtract 4 from both sides.
x - 4 = (1/2)y
Multiply each term 2.
2x - 8 = y
Plug f^-1(x) in for y.
f^-1(x) = 2x - 8

f^-1(4) = 2(4) - 8
f^-1(4) = 0
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What are the amplitude, period, and midline of f(x)=-4 cos (2x-n)+3?
tangare [24]
To find the amplitude and period you need to be familiar with the following equation. Also you need to know that the standard cos has a period of 2\pi and the midline is a line that runs between the max and min of the y-values of the function.

Equations:
f(x) = A cos(Bx +C) + D
f(x) = -4 cos(2x -n) + 3

A = amplitude = |-4| = 4
B = 2
C = phase shift = n = 0 
D = vertical shift = midline = 3

Amplitude = 4

Find the period:
Period = \frac{2\pi}{B} = \frac{2\pi}{2} = \pi

Find the midline:
We know that the amplitude is 4  so we have a range from -4 to 4. The standard y = cos(x) has its midline at 0 so y = 0. This is also true for y = -4 cos(x). In your equation though, you have a vertical shift of +3 so this changes our midline. With an amplitude of 4, which gives us a range from -4 to 4(our y-values), the shift moves this up by 3 so that means we will have new y-values and a range of -1 to 7. Now we need to find the midline(the middle of our y-values) of our new range. We can find this by using the following formula
Midline = \frac{Y_1 + Y_2}{2} = \frac{-1+ 7}{2} = \frac{6}{2} = 3

Midline:
y = 3

Note, in the following equations that D = 3 = midline

y = A (Bx+C) + D
y = -4 (2x + n) + 3

Also, the picture that is attached is what your equation looks like when graphed.


7 0
4 years ago
Does (3/2)^2 equal 2
Viktor [21]

Answer:

no

Step-by-step explanation:

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3 0
3 years ago
Solve for x: 1/2x + 4 = 9
Artist 52 [7]

Answer:

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1/2x +4=9

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x= 2 1/2 or 2.5

7 0
4 years ago
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