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Amiraneli [1.4K]
1 year ago
15

Help answer all please wrong answers will get reported

Mathematics
1 answer:
Maurinko [17]1 year ago
5 0

If f^{-1}(x) is the inverse of f(x), then by definition of inverse functions,

\left(f\circ f^{-1}\right)(x) = f\left(f^{-1}(x)\right) = x

Given f(x) = 2x-8, the inverse, if its exists, satisfies the equation above. Evaluate f at the inverse, we have

f\left(f^{-1}(x)\right) = 2 f^{-1}(x) - 8 = x

Solve for the inverse:

2 f^{-1}(x) - 8 = x

2 f^{-1}(x) = x + 8

\boxed{f^{-1}(x) = \dfrac12 x + 4}

Given g(x) = \frac13 x + 5, we do the same thing as before to find its inverse.

g\left(g^{-1}(x)\right) = \dfrac13 g^{-1}(x) + 5 = x \implies \boxed{g^{-1}(x) = 3x - 15}

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Answer: https://www.coursehero.com/file/36434863/math-124docx/

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6 0
3 years ago
48,919 ÷ ? = 489.19<br> 489,190 ÷ 1,000 =?<br> 4,891,900 ÷ ? = 489.19<br> ? ÷ 100,000 = 489.19
musickatia [10]

Answer:

  • 100
  • 489.190
  • 10,000
  • 48,919,000

Step-by-step explanation:

Each factor of 10 in the divisor causes the decimal point to move 1 place to the left.

a) The decimal point has moved 2 places to the left. The divisor is 10^2 = 100.

b) The divisor is 10^3, so the decimal point will move 3 places to the left.

  489.190

c) The decimal point has moved 4 places to the left, so the divisor is 10^4 = 10,000.

d) The divisor is 10^5, so the decimal point in the quotient if 5 places to the left of where it is in the dividend. Moving the quotient's decimal point 5 places to the right gives ...

  48,919,000

_____

<em>Additional comment</em>

An exponent signifies repeated multiplication. Here, we're concerned with repeatedly multiplying (or dividing) by factors of 10. The exponent indicates the number of factors: 10·10 = 10^2 = 100. It also matches the number of zeros following the 1 in the product. 1000 = 10^3 has 3 zeros after the 1, for example.

3 0
2 years ago
What is 1099 divide by 54
schepotkina [342]
1099/54=20.35185185185185
4 0
3 years ago
Read 2 more answers
PLEASE NO LINKS I LOST SO MANY POINTS
Ann [662]

Answer:

We will split the trapezoid into right angle triangle and rectangle

Traingle with base 3cm and height 10 - 6 = 4cm

Area of traingle

       = \frac{1}{2}*base *height = \frac{1}{2} * 3 * 4 = 6cm^{2}

Area of rectangle with sides 6cm and 3cm

       =6 * 3 = 18cm^{2}

Therefore, area of the trapezoid

       = 6+18 = 24cm^{2}

Area of the semi circle with radius 3/2 = 1.5cm

        = \frac{1}{2}\pi r^{2}  = \frac{1*\pi *1.5*1.5}{2} = 1.125\pi cm^{2}

Total area = 24 + 1.125\pi =27.53cm^{2}

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3 years ago
What is the converse of “if it is raining then we will not go the the beach
Dmitrij [34]
If we do not go to the beach, it is raining
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