Find f(x+2), if f(x)=-x²+2x+5.

Functions are a set of rules which determines the relation between dependent and independent variables. For every value for the independent variable, there must exist a unique value of the dependent variable which can be derived through the function.

Functions can also be thought of as a process in which for a given input there exists a specific output.

If a variable y is dependent on an independent variable x that makes x and y related and for some or every value of x, there is a unique value for y which is defined in the specific domain, then it is said that y is functionally dependent on the independent variable x.

A function f(x) where x is the independent variable and values of f(x) change according to the change in values of x. f(x) can also be written as the dependent variable y.

Therefore, y = f(x)

Let's solve the given problem.

f(x) = - x² + 2x + 5

we need to find f(x + 2)

Replacing x with (x + 2)

f(x + 2) = - (x + 2)² + 2 (x + 2) + 5

f(x + 2) = - (x² + 4x + 4) + 2x + 4 + 5

f(x + 2) = -x² - 4x - 4 + 2x + 4 + 5

f(x + 2) = -x² + (-4x + 2x) + (-4 + 4 + 5)

f(x + 2) = -x² - 2x + 5

Therefore, f(x + 2) = -x² - 2x + 5

Hence the value of f(x + 2) when f(x) = -x² + 2x + 5 is f(x + 2) = -x² - 2x + 5

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