# Functions : Parabolas and Difference Quotient

1. Given that f(x) = x^2 - x +4 and g(x) = (sqr root x) +2 find (f o g)(x)

2. Find the equation of the parabola with focus F(12,20) and directrix y = 10

3. For f(x) = 1/ (x -2) , find and simplify the difference quotient (f(3+h) -f(3)) / h

https://brainmass.com/math/graphs-and-functions/functions-parabolas-difference-quotient-9433

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1. Given that f(x) = x^2 - x +4 and g(x) = (sqr root x) +2 find (f o g)(x)

2. Find the equation of the parabola with focus F(12,20) and directrix y = 10

3. For f(x) = 1/ (x -2) , find and simplify the difference quotient (f(3+h) -f(3)) / h

Solutions:

1-

(f o g)(X)= f(g(x))

It means consider the function f acting on g(x) instead of x. What does f do on x?

f(x)= ...

#### Solution Summary

An equation of a parabola is found and a difference quotient is simplified.