Can someone simplify this problem?

Question

Given f(x) = -2x^2 -7 and g(x) = x-1 find and simplify

(g-f)(x)
(g-f)(-1)
f[g(x)]
f[g(-1)]

Answer 1

(g-f)(x)
= g(x) - f(x)
= (x - 1) - (-2x^2 - 7)
= x - 1 + 2x^2 + 7
= 2x^2 + x + 6

(g-f)(-1)
ok... (g-f)(x) = 2x^2 + x + 6, so plug in (-1) for x and solve...
2(-1)^2 + (-1) + 6
= 2 - 1 + 6
= 7

f[g(x)]
= f(x - 1)
= -2(x-1)^2 - 7
= -2(x^2 - 2x + 1) - 7
= -2x^2 + 4x - 2 + 7
= -2x^2 + 4x + 5

f[g(-1)]
Now that you have f[g(x)], which I just solved for you above, plug in (-1) for x and solve.

Answer 2

First let me explain wat f(x) means.
This function f can be considered as operation on x. e.g
if function is square than
square(x) = x^2
root(x) = x^(1/2)....etc

and using some rules lets solve the problem and simplify:

1) (g-f)(x) = g(x)-f(x)
-> x-1 -(-2x^2 -7)
x-1 + 2x^2+7
2x^2+x+6


2) (f-g)(-1)
2*(-1)^2+(-1)+6
2-1+6
7

3) f[g(x)]
f(x-1)
-2(x-1)^2 -7
-2(x^2+1-2x)-7
-2x^2-2+4x-7
-2x^2+4x-9

4) f[g(-1)]
-2*-1^2+4*(-1)-9
-2-4-9
-15

Answer 3

Errrmm..... I don't want to seem as if I'm being overly picky.... But find and simplify --what--?

Doug

Answer 4

Find what?

fog........fog = f(g(x))

==> -2(x - 1)^2 - 7

Expand this out....if....this is what you're looking for.

Answer 5

find and simplify what?

Answer 6

uhhh.....there isn't much to simplify- because there is nothing to do.

Answer 7

ur missing the relationship between f(x) and g(x)!

Answer 8

LOL!