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frosja888 [35]
4 years ago
11

Can anyone help me?

Mathematics
1 answer:
Korolek [52]4 years ago
8 0
I think it's a weak postitive correlation
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F:[1/2,infinity)—&gt;[3/4,infinity) <br> f(x)=x^2-x+1 <br> find the inverse of f(x);please explain
dexar [7]

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}

8 0
3 years ago
Derivative of (a^x/Log a)?​
Zolol [24]
<h2>\large\bold{\underline{\underline{To \: \:  Differentive:-}}}</h2>

\sf{\dfrac{a^x}{log(a)} }

<h3>(OR)</h3>

\sf{\dfrac{a^x}{ln(a)} }

<h2>\large\bold{\underline{\underline{Solution:-}}}</h2>

\sf{Let\ y=\dfrac{a^x}{ln(a)} }

\sf{=\dfrac{d}{dx}\bigg[\dfrac{a^x}{ln(a)}  \bigg] }

<h3>(Linear differentiation)</h3>

\sf{=\dfrac{1}{ln(a)}.\dfrac{d}{dx}(a^x)  }

\sf{=\dfrac{ln(a)a^x}{ln(a)} }

\boxed{\sf{=a^x}}

<h2>\large\bold{\underline{\underline{Applied:-}}}</h2>

<h3>✭ Linear differentiation</h3>

→ \sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}

<h3>✭ Exponential function rule</h3>

→ \sf{(a^x)'=ln(a).a^x}

3 0
3 years ago
Read 2 more answers
What is the angle of pdh
s344n2d4d5 [400]
PDH+HDF=180
PDH+129=180
PDH= 51
3 0
4 years ago
Let f(n) be the average number of days a house stays on the market before being sold for price p in $1,000s, which statement bes
denis23 [38]

Answer:

b

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
This is worth 25 points... plz answer. What is a RATIO?
sleet_krkn [62]

A ratio is like say there are 25 boys as to 23 girls or its a comparison in the number of things of different objects or like for every 2 cats there 1 dog


7 0
3 years ago
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