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Georgia [21]
3 years ago
8

F:[1/2,infinity)—>[3/4,infinity) f(x)=x^2-x+1 find the inverse of f(x);please explain

Mathematics
1 answer:
dexar [7]3 years ago
8 0

Answer:

f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

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

This allows me to write the right hand side as a square.

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

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

\pm \sqrt{y-3/4}=x-1/2

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

\sqrt{y-3/4}=x-1/2

Add 1/2 on both sides:

1/2+\sqrt{y-3/4}=x

The last step is to switch x and y:

1/2+\sqrt{x-3/4}=y

y=1/2+\sqrt{x-3/4}

f^{-1}(x)=1/2+\sqrt{x-3/4}

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3 years ago
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erica [24]

Answer:

2.2 metres squared

Step-by-step explanation:

We need to find the area of this trapezoid.

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Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.

Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:

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<em>~ an aesthetics lover</em>

8 0
3 years ago
What is the difference?
matrenka [14]

Answer:

The Difference in mathematical terms is the result of subtracting one number from another.

Step-by-step explanation:

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Help me, please. Please also explain to me why you picked your answer.
Shkiper50 [21]

Answer: Lower left corner  \frac{29}{18+29} \times 100

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4 0
3 years ago
Read 2 more answers
13 + 31 = 24 not 44 how on earth is this possible all help is great. Thanks.
Aneli [31]
It is 44. Can't argue about that
3 0
3 years ago
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