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Rashid [163]
3 years ago
5

The function f(x) = 9x +5 is one-to-one. Find an equation for f-'(x), the inverse function.

Mathematics
1 answer:
Gnesinka [82]3 years ago
8 0

Answer:

The inverse function is f^{-1}(x) = \frac{x - 5}{9}

Step-by-step explanation:

Inverse function:

Suppose we have a one-to-one function y = f(x). To find it's inverse, we exchange y and x, and then isolate y.

In this question:

y = 9x + 5

Exchanging x and y:

x = 9y + 5

Isolating y:

9y = x - 5

y = \frac{x - 5}{9}

f^{-1}(x) = \frac{x - 5}{9}

The inverse function is f^{-1}(x) = \frac{x - 5}{9}

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Write the following fraction as a decimal 6/5
steposvetlana [31]

Answer:1.2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
10. When a rubber ball is dropped from a height, h cm on to a flat concrete floor, it rebounds to 3 5 h cm a height of Given a r
Xelga [282]

Step-by-step explanation:

Let the height above which the ball is released be H

This problem can be tackled using geometric progression.

The nth term of a Geometric progression is given by the above, where n is the term index, a is the first term and the sum for such a progression up to the Nth term is

To find the total distance travel one has to sum over up to n=3. But there is little subtle point here. For the first bounce ( n=1 ), the ball has only travel H and not 2H. For subsequent bounces ( n=2,3,4,5...... ), the distance travel is 2×(3/4)n×H

a=2H..........r=3/4

However we have to subtract H because up to the first bounce, the ball only travel H instead of 2H

Therefore the total distance travel up to the Nth bounce is

For N=3 one obtains

D=3.625H

7 0
2 years ago
7 is 1/10 of what number
umka21 [38]
We should find the original number, 7 of 1/10. We divide the known number for the numerator, than multiply for denominator.

7 : 1 = 7 * 10 = 70 <- answer

So 7 is 1/10 of 70

We can check our work:

1/10 of 70 = 7?

70 : 10 = 7*1 = 7
3 0
3 years ago
-6(x+7)=-4x-2<br> How many solutions does it have
geniusboy [140]

Answer:

Equation have Unique solution i.e x=-20

Step-by-step explanation:

Given Equation:

-6(x+7)=-4x-2

Solving the Equation for 'x'.

           -6(x)-6(7)=-4x-2\\\\-6x-42=-4x-2

Adding '4x'  both sides:

             -6x+4x-42=-4x+4x-2\\\\-6x+4x-42=-2\\\\-2x-42=-2

Adding '42' both sides:

               -2x-42+42=-2+42\\\\-2x=40

                        x=\frac{40}{-2} \\\\x=-20

The equation have Unique solution with the value of x=-20

6 0
3 years ago
-X² + 5x - 6 = 2<br> Using the quadratic formula
Ivenika [448]

-x^2+5x-6=2\\-x^2+5x-6-2=0\\-x^2+5x-8=0\\

↝ Form into ax^2+bx+c = 0 where a > 0 (Optional)

x^2-5x+8=0 ↝ Multiply -1 for both sides.

↝ Then proceed with the Quadratic Formula.

x = [-b ± (√b²-4ac)]/2a ↝ Quadratic Formula

x=\frac{-(-5)+-\sqrt{(-5)^2-4(1)(8)}}{2(1)}\\x=\frac{5+-\sqrt{25-32}}{2}\\

↝ As you can see that inside the square root, the numbers cannot be negative. Therefore, the solutions are imaginary.

↝ Solution with Real Numbers  System ↝  There are no real solutions.

↝ Solution with Complex Number System ↝

x=\frac{5+-\sqrt{25-32}}{2}\\x=\frac{5+-\sqrt{-7}}{2}\\x=\frac{5+-\sqrt{7}i }{2}

Therefore, the answer for Complex Number System is (5±√7i)/2

3 0
2 years ago
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