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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).

1 Answer

4 votes

Answer:


f(x)=((√(x)+x+3)^2+2+x)/(x^2+2)

Explanation:

We have to find the formula for f(x)

Let x be the number

According to question

Now,


√(x)+x+3

Now,

After squaring we get


(√(x)+x+3})^2

Add x+2 to above result then, we get


(√(x)+x+3})^2+2+x

Then,


((√(x)+x+3)^2+2+x)/(x^2+2)

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


f(x)=((√(x)+x+3)^2+2+x)/(x^2+2)

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