Question

F(x) = 3x + 6 please help quickly!!!!!!!

Answer 1

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:

1. f(a)
2. f(a + h), and
3. $\frac{(f(a + h) - f(a)) }{h}$

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:

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

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