Question

A function f is given by f(x)=1/(x+2)^2 This function takes a number x, adds 2, squares the result, and takes the reciprocal of that result. Find f(4), f(0), f(a), f(x + h), and f(x+h) - f(x)/h Find f(4). f(4) =----- (Simplify your answer.)

Answer 1

The value of f(4) is 1/36. The values of f(0), f(a), and f(x + h) depend on the specific values of 'a', 'x', and 'h'. The expression f(x+h) - f(x) / h cannot be simplified without knowing the specific values of 'h' and 'x'.

Step-by-step explanation:

To find f(4), we substitute 4 into the function f(x) and evaluate:

f(4) = 1 / (4 + 2)^2

f(4) = 1 / 6^2

f(4) = 1 / 36

Therefore, f(4) = 1/36.

For the remaining parts of the question, let's go step by step:

f(0):

f(0) = 1 / (0 + 2)^2

f(0) = 1 / 2^2

f(0) = 1 / 4

Therefore, f(0) = 1/4.

f(a):

f(a) = 1 / (a + 2)^2

There is no simplification we can do here since we don't know the specific value of 'a'.

f(x+h):

f(x+h) = 1 / (x + h + 2)^2

f(x+h) - f(x) / h:

f(x+h) - f(x) / h = (1 / (x + h + 2)^2 - 1 / (x + 2)^2) / h

There are no further simplifications we can do without knowing specific values for 'h' or 'x'.

Learn more about Evaluating a Function