SOLUTION: GIVEN THE FUNCTIONS F(X)= 3X^2-5X+4, G(X)=3X/X-2, H(X)=THE SQUARE ROOT OF 2-X FIND: F(X-1), G(X+H), AND H(X+2). COULD YOU SHOW ME STEP BY STEP HOW YOU WOULD SOLVE THESE PROBL

Question 118535: GIVEN THE FUNCTIONS F(X)= 3X^2-5X+4, G(X)=3X/X-2, H(X)=THE SQUARE ROOT OF 2-X FIND:
F(X-1), G(X+H), AND H(X+2). COULD YOU SHOW ME STEP BY STEP HOW YOU WOULD SOLVE THESE PROBLEMS? THANK YOU VERY MUCH

Found 3 solutions by stanbon, solver91311, MathLover1:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
GIVEN THE FUNCTIONS
F(X)= 3X^2-5X+4
F(X-1) = 3(X-1)^2-5(X-1)+4
= 3(x^2-2x+1)-5x-5+4
= 3x^2-6x+3-5x-1
= 3x^2-11x+2
-----------------------
G(X)=3X/X-2
G(x+h) = 3(x+h)/x+h-2
= [3x+3h]/[x+h-2]
----------------------
H(X)=THE SQUARE ROOT OF 2-X
H(X+2) = sqrt(2-(x+2))
= sqrt(-x)
==================
Cheers,
Stan H.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
(Please do not type your questions in ALL CAPS. It is hard to read, annoying, and is the electronic equivalent of SHOUTING.)

A:

In the expression for , substitute every place you see , thus:

Then expand and simplify by collecting terms:

B:

What is ? , so .

Again, take the definition of and substitute every place you see .

(I'm not sure I even want to begin to try to simplify that horror. I'd just leave it be and hope for the best)

There is also the possibility that I misinterpreted your expression for . In the event that you actually meant , this problem comes out quite differently.

, then

Rationalizing the denominator:

C:

Do this one exactly the same way I did the first one. Take and substitute everywhere you see . I'll let you finish.

Super-Double-Plus Extra Credit: What is the domain of ?

Hope that helps.
John
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
1.

Find

2.

Find

Find

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