Given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and $\frac{(f(a + h) - f(a)) }{h}$ by substituting their values into f(x) = 3x + 6. We will have the following:

$\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}$

Given:

f(x) = 3x + 6

We are told to find:

f(a)
f(a + h), and
$\frac{(f(a + h) - f(a)) }{h}$

1. Find f(a):

Substitute x = a into f(x) = 3x + 6

f(a) = 3(a) + 6

f(a) = 3a + 6

2. Find f(a + h):

Substitute x = a + h into f(x) = 3x + 6

f(a + h) = 3(a + h) + 6

f(a + h) = 3a + 3h + 6

3. Find $\frac{(f(a + h) - f(a)) }{h}$ :

Plug in the values of f(a + h) and f(a) into $\frac{(f(a + h) - f(a)) }{h}$

Thus:

$\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\$

Add like terms

$\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}$

Therefore, given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and $\frac{(f(a + h) - f(a)) }{h}$ by substituting their values into f(x) = 3x + 6. We will have the following:

$\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}$

Learn more here:

brainly.com/question/8161429

6 0

2 years ago

-1/6 + 4/5 Write your answer in simplest form

Alchen [17]

Answer:19/30

Step-by-step explanation:

1. multiply and divide(left to right)-1/6

=-1/6+4/5

2.multiply and divide(left to right)4/5

=-1/6+4/5

3. add and subtract(left to right)-1/6+4/5=19/30

=19/30

5 0

2 years ago

Someone pls help me i can’t pass this quiz lol

Sophie [7]

Answer:

60ft

Step-by-step explanation:

h x 20 = 120

h=120/20

h=60

8 0

2 years ago