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QuestionFind f(6+h)f(6+h) for f(x)=∣x−6∣x−6f(x)=\frac{|x-6|}{x-6} when h<0h<0.

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=∣x−6∣x−6f(x)=\frac{|x-6|}{x-6} . We are asked to find f(6+h)f(6+h) where h<0h<0.

STEP 2

First, we need to substitute 6+h6+h into the function f(x)f(x).
f(6+h)=∣6+h−6∣6+h−6f(6+h)=\frac{|6+h-6|}{6+h-6}

STEP 3

implify the expression inside the absolute value and the denominator.
f(6+h)=∣h∣hf(6+h)=\frac{|h|}{h}

STEP 4

Since h<0h<0, the absolute value of hh is −h-h. Substitute this into the equation.
f(6+h)=−hhf(6+h)=\frac{-h}{h}

STEP 5

implify the equation to find the value of f(+h)f(+h).
f(+h)=−hh=−1f(+h)=\frac{-h}{h} = -1So, f(+h)=−1f(+h) = -1 when h<0h<0.

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