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