Question

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).

Answer 1

`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)`