find the following

if x =x^2+2

f(3/2) 4.24
f(b) 0

Thank you

To find the values of f(3/2) and f(b) given the equation x = x^2 + 2, we can substitute the given values of x and solve for f(x).

Let's start with finding f(3/2):

Step 1: Substitute x = 3/2 in the equation x = x^2 + 2.
3/2 = (3/2)^2 + 2

Step 2: Simplify the equation.
3/2 = 9/4 + 8/4
3/2 = 17/4

Step 3: Convert the right-hand side to a decimal.
3/2 ≈ 1.5
17/4 ≈ 4.25

Therefore, f(3/2) ≈ 1.5 and f(3/2) ≈ 4.25. (Please note that the expected answer 4.24 seems to be rounded to two decimal places. Rounded to two decimal places, it would be 4.25.)

Now let's find f(b):

Step 1: Substitute x = b in the equation x = x^2 + 2.
b = b^2 + 2

Step 2: Move all terms to one side to write it in a quadratic equation form.
b^2 - b + 2 = 0

Step 3: Since we are looking for the value of b when f(b) = 0, we need to solve the quadratic equation for its roots.

Unfortunately, without additional information or context, we cannot determine the exact value of b that satisfies the equation. It would depend on the specific values you are given or any additional equations or conditions that define the relationship between b and x.

In summary:
- f(3/2) is approximately 1.5.
- f(b) cannot be determined without more information or context.