Respuesta :

akposevictor

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

[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]

Given:

  • f(x) = 3x + 6

We are told to find:

  1. f(a)
  2. f(a + h), and
  3. [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]

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 [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]:

  • Plug in the values of f(a + h) and f(a) into [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]

Thus:

[tex]\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\[/tex]

  • Add like terms

[tex]\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}[/tex]

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

[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]

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