f(x) and g(x) UGH!!!!!

[perilous]

Okay, I know this is supposed to be easy, but somehow when I work out these problems none of them are coming out right(well I'm still trying to figure out how I got the ones on the last assignment wrong :shock: )
here goes:
f(x)=2x^2-x+1 and g(x)=-x+1 find:
(f-g)(2)
(f+g)(0)
(f/g)(-1)
(fg)(0)
(fog)(-1)
(f-g)(x)
and the one that I don't even think I remember from class!!
if f(x)=x+1/x-1 and g(x)= square root 2x+1/2 find the domain of (fog)(x).

thanks for any help, maybe a push in the right direction will help..some

 

[soroban]

Hello, perilous!

Believe it or not, the first four are Algebra 1 problems . . .

f(x) = 2x² - x + 1 and g(x) = -x + 1

Find: .(a) (f - g)(2) . . (b) (f + g)(0) . . (c) (f/g)(-1) . . (d) (fg)(0)

(a) The function (f - g)(x) means: .f(x) - g(x)
. . . So do the algebra: .f(x) - g(x) .= .(2x² - x + 2) - (-x + 1) .= .2x² + 1
. . . . . Hence: .(f - g)(x) .= .2x² + 1
. . . (f - g)(2) means "let x = 2".
. . . . . Therefore: .(f - g)(2) .= .2·2² + 1 .= .9

(d) The function (fg)(x) means: .f(x)·g(x)
. . . Do the algebra: .f(x)·g(x) .= .(2x² - x + 1)(-x + 1) .= .-2x³ + 3x² - 2x + 1
. . . . . Hence: .(fg)(x) .= .-2x³ + 3x² - 2x + 1
. . . (fg)(0) means "let x = 0".
. . . . . Therefore: .(fg)(0) .= .-2·0³ + 3·0² - 2·0 + 1 .= .1

Think you can do (b) and (c) now?

 

[Denis]

In case you get confused, soroban made an unpardonable typo in part a):
So do the algebra: f(x) - g(x) = (2x^2 - x + 2) - (-x + 1) = 2x^2 + 1 ; should be:
So do the algebra: f(x) - g(x) = (2x^2 - x + 1) - (-x + 1) = 2x^2

This will be duly noted on his file flap and seriously affect his annual performance review,
probably resulting in a demotion to moderator.

 

[perilous]

thanks!!