SOLUTION: Please help! Help I do not understand this at all. I read over the chapter numerous times and still confused. We define the following functions: f(x)=2x+5 g(x)=x^2-3

Algebra ->  Rational-functions -> SOLUTION: Please help! Help I do not understand this at all. I read over the chapter numerous times and still confused. We define the following functions: f(x)=2x+5 g(x)=x^2-3       Log On


   

Question 767979: Please help!
Help I do not understand this at all. I read over the chapter numerous times and still confused.
We define the following functions:
f(x)=2x+5
g(x)=x^2-3
h(x)=7-x/3

o Compute (f – h)(4).
o Evaluate the following two compositions: (fog)(x)and (hog)(x) .
o Transform the g(x) function so that the graph is moved 6 units to the right and 7 units down.
o Find the inverse functions f^-1(x) and h^-1(x) .
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The goal is to learn to use function notation and apply definitions of functions and function notation.

Looking at the first task, (f-h)(4), seems to be just take the two functions, f and h, form their difference, and then evaluate this resulting function at x=4.

f%28x%29-h%28x%29=2x%2B5-%287-x%2F3%29
=2x%2B5-7%2Bx%2F3
2x-2%2Bx%2F3
2%2A3x%2F3-2%2A3%2F3%2Bx
%286x-6%2Bx%29%2F3
highlight%28%28f-h%29%28x%29=%287x-6%29%2F3%29

At x=4, the function becomes
%28f-h%29%284%29=%287%2A4-6%29%2F3=%2828-6%29%2F3=highlight%2822%2F3%29