Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the foll...

Question

Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6.

ƒ(x + 2)

Accepted Answer

Hello, today we're going to be evaluating F of X plus five for the given function below. So the function given to us is F of X is equal to negative 11, X plus 31. Now, in order to evaluate F of X plus five, we're going to need to plug in the quantity X plus five into the function F of X. What this means is that we're going to be replacing every variable X and F of X with the new input value, which will be X plus five. So if we input X plus five into mth of X, the new function that we are left with is negative 11 multiplied by X plus five plus 31. Now, what we'll need to do is we'll need to algebraically simplify F of X plus five. In order to simplify the function, we're going to need to distribute negative 11 into the quantity X plus five, negative 11 multiplied by X will give us negative X and negative 11 multiplied by five will leave us with negative 55 and we have 31 at the end of the function. Finally negative 55 plus 31 will leave us with the value of negative 24. So the simplified form of F of X plus five will be negative X minus 24. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(x + 2)