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Ymorist [56]
2 years ago
10

Consider the function below. g(x) = 4x − 1 Find the difference quotient below (where h ≠ 0) and simplify your answer. g(x + h) −

g(x) -------------------- h
Mathematics
1 answer:
eimsori [14]2 years ago
3 0

Answer:

The difference quotient is 4.

Step-by-step explanation:

Given that:

g(x) = 4x - 1

To find:

Difference quotient = ?

where h \neq 0

Solution:

Formula for Difference quotient is given as:

\dfrac{g(x+h)-g(x)}{h}

First of all, let us find out g(x+h)

Replacing x with x+h

g(x+h) = 4(x+h)-1 \\\Rightarrow g(x+h) = 4x+4h-1

Now,

g(x+h)-g(x) = (4x+4h-1 )-(4x-1)\\\Rightarrow g(x+h)-g(x) = 4x+4h-1 -4x+1\\\Rightarrow g(x+h)-g(x) = 4h

Putting the above value in:

\dfrac{g(x+h)-g(x)}{h} = \dfrac{4h}{h}

We are given that, h \neq 0

\therefore \dfrac{4h}{h}  = 4

So, the difference quotient is 4.

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