Expert: Sherman D. - 7/25/2009

Question
QUESTION: HELP!  I have no idea how to do these.  Can you walk me thru this please??

1. let f(x) - 2x^2+3 and g(x)= -3x+1.  Find the rule for the function f-g

2. If f(x) = 1/x+2, find and simplify f(a+h) -f(a)/h  (h=0)

Keep in mind the h=0 - the equals sign has a slash thru it.  Does that make sense?

THANK YOU!!!


ANSWER: 1.)
f(x) = 2x^2 + 3
g(x) = -3x + 1

f - g = (2x^2 + 3) - (-3x + 1)
f - g = 2x^2 + 3 + 3x - 1
f - g = 2x^2 + 3x + 2

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2.)
f(x) = 1/(x + 2)

if h = 0, then the problem cannot be defined.

---------- FOLLOW-UP ----------

QUESTION: HI again:
'h' does NOT equal 0.  The '=' sign had a slash thru it, so I guess that means that h "does not" equal 0?

Does that make sense?

Answer
oh ok

f(x) = 1/(x + 2)

(f(a + h) - f(a))/h
h ≠ 0, thats the symbol you could had used.

((1/(a + h + 2)) - (1/(a + 2)))/h

(((a + 2) - a - h - 2)/((a + 2)((a + 2) + h)))/h

(-h/((a + 2)^2 + (a + 2)h))/h

-h/h((a + 2)^2 + (a + 2)h))

-1/((a + 2)^2 + (a + 2)h)