Mathematics: 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

Answer is a because you got 3/8 squares that are shaded but if you time both but 3 you get 9/24...

Consider the function below. g(x) = 4x − 1 Find the

jennaranelli05

31.01.2022

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 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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