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QuestionEvaluate (gf)(1)\left(\frac{g}{f}\right)(1) for f(x)=−4xf(x)=-4x and g(x)=∣x+7∣g(x)=|x+7|. Provide your answer as an integer.

Studdy Solution

STEP 1

Assumptions1. The function f(x)=−4xf(x)=-4x . The function g(x)=∣x+7∣g(x)=|x+7|
3. The function h(x)=1x−5h(x)=\frac{1}{x-5}
4. We need to evaluate the function (gf)(1)\left(\frac{g}{f}\right)(1) for x=1x=1

STEP 2

The function (gf)(x)\left(\frac{g}{f}\right)(x) is defined as g(x)f(x)\frac{g(x)}{f(x)}. So, we need to find the values of g(1)g(1) and f(1)f(1).

STEP 3

First, let's find the value of g(1)g(1) by substituting x=1x=1 into the function g(x)g(x).
g(1)=∣1+7∣g(1) = |1+7|

STEP 4

Calculate the absolute value.
g(1)=∣8∣=8g(1) = |8| =8

STEP 5

Now, let's find the value of f(1)f(1) by substituting x=1x=1 into the function f(x)f(x).
f(1)=−4×1f(1) = -4 \times1

STEP 6

Calculate the value.
f(1)=−4f(1) = -4

STEP 7

Now that we have the values of g(1)g(1) and f(1)f(1), we can substitute these into the function (gf)(1)\left(\frac{g}{f}\right)(1).
(gf)(1)=g(1)f(1)=−4\left(\frac{g}{f}\right)(1) = \frac{g(1)}{f(1)} = \frac{}{-4}

STEP 8

Calculate the value.
(gf)(1)=−2\left(\frac{g}{f}\right)(1) = -2The value of the function (gf)(1)\left(\frac{g}{f}\right)(1) for x=1x=1 is −2-2.

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