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ArbitrLikvidat [17]
3 years ago
12

Find the inverse of the given function f(x) =2^x+6

Mathematics
1 answer:
ruslelena [56]3 years ago
8 0

Answer:

f^{-1}(x) = log_2(x-6)

Step-by-step explanation:

To find the inverse f^{-1}(x) of a function follow the following steps.

1) Do y = f (x)

f(x) =y= 2 ^ x + 6

y= 2 ^ x + 6

2) Solve the equation for the variable x.

y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)

3) exchange the variable y with the variable x

x=log_2(y-6)\\\\y=log_2(x-6)

Finally the inverse is:

f^{-1}(x) = log_2(x-6)

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Solve: x=4+(4x-4)1/2
Damm [24]

Answer:

x = 10

Step-by-step explanation:

x = 4 + (4x-4) ^ (1/2)

First, we rewrite the expression:

x = 4 + (4x-4) ^ (1/2)

x = 2 (2+ (x-1) ^ (1/2))

x = 4 + 2 (x-1) ^ (1/2)

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To check it we substitute x = 10 in the expression:

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8 0
3 years ago
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Which system of inequalities is represented by the graph?
timofeeve [1]

Answer:

The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D

Step-by-step explanation:

To find the answer let us find the equation of each line

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∵ The line passes through points (5 , 0) and (0 , 2.5)

- Find the slope of the line

∵ m = Δy/Δx

∴ \frac{0-2.5}{5-0}=\frac{-2.5}{5}

∴ m = -0.5

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∵ y = 2.5 at x = 0

∴ b = 2.5

- Write the equation of the line

∴ y = - 0.5 x + 2.5

- Multiply both sides by 2

∴ The equation of the blue line is 2 y = - x + 5

- The shading is under the line and the line is solid, that means

  2 y is less than or equal - x + 5

∴ The inequality of the blue line is 2 y ≤ - x + 5

Red line:

∵ The line passes through points (3 , -5) and (0 , 4)

- Find the slope of the line

∴ m=\frac{-5-4}{3-0}=\frac{-9}{3}

∴ m = -3

∵ y = 4 at x = 0

∴ b = 4

- Write the equation of the line

∴ y =  -3 x + 4

∴ The equation of the red line is y = -3 x + 4

- The shading is below the line and the line is solid, that means

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Let us find which answer is the same with this system of inequalities

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- Add x to both sides

∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D

∵ y ≤ -3 x + 4

- Add 3 x to both sides

∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D

The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph

4 0
3 years ago
The rectangle below is enlarged using a scale factor of 1.5. What will be the new length and width of the rectangle?
Likurg_2 [28]

Answer: length = 4.5 m, width = 3 m

Step-by-step explanation:

When a shape is enlarged using a scale factor, you simply multiply each of the sides by the scale factor.

length = 3 * 1.5 = 4.5 m

width = 2 * 1.5 = 3 m

5 0
3 years ago
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