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

Answer:

$f(x)=\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}$

Step-by-step explanation:

We have to find the formula for f(x)

Let x be the number

According to question

Now,

$\sqrt{x}+x+3$

Now,

After squaring  we get

$(\sqrt{x}+x+3})^2$

Add x+2 to above result then, we get

$(\sqrt{x}+x+3})^2+2+x$

Then,

$\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}$

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

$f(x)=\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}$