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Georgia [21]
2 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]2 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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Given the formula for an arithmetic sequence f(7) = f(6) + 4 written using a recursive formula, write the sequence using an arit
natita [175]

Answer:

Of(7) = f(1) + 24

Step-by-step explanation:

Since this Arithmetic Sequence can be written recursively as a function, then we can write the whole sequence, by adding the common difference to the previous function. So writing it as an Arithmetic formula is (placing an example, with a common difference of 4 units):

\left.\begin{matrix}n &1&2&3&4&5&6 &7\\f(n)&2&6&10 & 14&18&22&26 \end{matrix}\right|\\f(n)=f(n-1)+d\:\: (Recursive \: Formula)\Rightarrow a_{n}=a_{n-1}+4\: \: \: (Arithmetic\: Formula)\\Of(7)=f(1)+6*4\Rightarrow a_{7}=a_{1}+(7-1)4\Rightarrow a_{7}=a_{1}+24\\

6 0
3 years ago
Read 2 more answers
Is anyone able to solve this?
Olenka [21]

Explanation:

To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:

a² + b² = c² (c is always hypotenuse)

So:

a² + 6² = 9²

a² = 9² - 6²

a² = 81 - 36

a² = 45

a = sqrt45

Now we do the same thing for the other triangle:

x² + 5² = sqrt45²

x² + 25 = 45

x² = 20

x = 2√5 or 4.5...

4 0
10 months ago
The value of <br> 37<br> −<br> −<br> √<br> −<br> 24<br> −<br> −<br> √<br> 37−24<br> is between:
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Answer:23 And 24

Step-by-step explanation:

((37 - (−√(−24))) - (−√(37))) - 24 =

19.0827625 + 4.89897949 i

19.0827625

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23.98174199 is between 23 and 24

3 0
3 years ago
HELP I NEED HELP WITH THIS
Elena-2011 [213]

Answer:

Step-by-step explanation:

4 0
3 years ago
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