Homework Help

If f(x) = 2x - 9, find f(p) and f(x + h).  

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mattlimey | Student, Grade 11 | (Level 2) Honors

Posted May 6, 2013 at 8:47 AM via web

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If f(x) = 2x - 9, find f(p) and f(x + h).

 

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted May 6, 2013 at 9:18 AM (Answer #1)

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and `p`  is the same as or

Multiply the exponent of (in this case 1) by the co-efficient of and then subtract 1 from the exponent (ie 1-1=0). As now has a zero power or exponent, it falls away.

`therefore f'(x) = 2 times 1 x ^(1-1)= 2x^0```

`therefore f'(x) = p = 2`

Using first principles to verify this answer:

 

 

Note we now have (x+h) -  (2x +2h -9)

 

Note how the symbol has changed (-9 becomes +9). Now simplify:

 

`therefore f'(x) = p = 2`

We have from the formula and in this case:

 

 

Please note that p = f ' (x) and therefore the question should be continued as follows:

f' (x) = p = 2

`therefore f(p) = f(2) ` 

Therefore f(p) = 2 (2)-9 = -5

Ans:

f(p)=  -5  

Sources:

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