For f(x) = , find f(-1)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should know that if the problem requests to find the value of any function at a given x, you need to substitute the given value for x and to check if the function exists for the given value of x.

Hence, considering `f(x) = 5x + 1` , you may evaluate `f(-1), ` substituting -1 for x in equation of function, such that:

`f(-1) = -5 + 1 => f(-1) = -4`

Notice that all functions that contain a denominator whose root is -1, does not exists at `x = -1` .

Considering the function `f(x) = (2x + 1)/(x + 1), ` you cannot evaluate f(-1), since `x = -1`  cancels the denominator.

If the equation of the function contains a square root, you need to check first if for `x = -1`  , the square root holds such that:

`f(x) = sqrt(x- 1)`

Notice that at `x = -1, f(-1) = sqrt(-2), ` which is invalid.

Hence, the main conclusion is that evaluating a function at `x = -1` , you need to check if the function exists at `x = -1`  and then you may evaluate  `f(-1)`  substituting -1 for x in equation of function.

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