Answered

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Let f(x) be defined on the positive real numbers as follows:

Start with a number x.
Take the square root of the number and add 3 more than the number you started with.
Square the result and add 2 more than the original number.
Finally, divide the result by 2 more than the square of the original number.

Required:
Write a formula for f(x).

Sagot :

Lublanaidn

Answer:

[tex]f(x)=\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}[/tex]

Step-by-step explanation:

We have to find the formula for f(x)

Let x be the number

According to question

Now,

[tex]\sqrt{x}+x+3[/tex]

Now,

After squaring  we get

[tex](\sqrt{x}+x+3})^2[/tex]

Add x+2 to above result then, we get

[tex](\sqrt{x}+x+3})^2+2+x[/tex]

Then,

[tex]\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}[/tex]

Therefore, the formula for f(x) is given by

[tex]f(x)=\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}[/tex]

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