Given f(x) = x^2 + 1 and g(x) = x-2
a. Find (f-g)(-2)
[f-g](x) = f(x) - g(x) = x^2-x+3
[f-g](-2) = (-2)^2-(-2)+3 = 9
----------------------------
b. Find f[g(5)]
f[g(5)] = f[5-2] = f[3] = 9+1 = 10
===================
problem a.
-----
(f-g)(x) = f(x) - g(x)
-----
(f-g)(-2) = f(-2) - g(-2)
-----
f(x) = x^2 + 1
f(-2) = (-2)^2 + 1
f(-2) = 4+1
f(-2) = 5
-----
g(x) = x-2
g(-2) = -2-2
g(-2) = -4
-----
f-g(-2) = f(-2) - g(-2) = 5 - (-4) = 5 + 4 = 9
-----
answer for a is:
f-g(-2) = 9
-----
problem b.
-----
g(x) = x-2
g(5) = 5-2
g(5) = 3
-----
f(x) = x^2 + 1
f(g(5)) = (g(5))^2 + 1
since g(5) = 3, equation becomes:
f(g(5)) = 3^2 + 1
f(g(5)) = 9 + 1 = 10
-----
answer for b is:
f(g(5)) = 10
-----
in general, you substitute whatever value is replacing x in the equation to get your answers.
looking at problem b in this way, we would get a general solution as follows:
f(x) = x^2 + 1
g(x) = x-2
substitute g(x) for x:
f(g(x)) = (g(x))^2 + 1
substitute the equation for g(x) on the right hand side.
f(g(x)) = (x-2)^2 + 1
remove parentheses:
f(g(x)) = x^2 - 4*x + 4 + 1
simplify:
f(g(x)) = x^2 - 4*x + 5
-----
substituting 5 for x:
f(g(5)) = (5^2 - 4*5 + 5
simplifying:
f(g(5)) = 25 - 20 + 5
f(g(5)) = 10
-----
answer is the same as above where we first solved for g(5) which became 3, and then substituted that value in f(g(x)) which made it f(3)).
Hope this helps!
Are you serious? oh well..
ok, draw a circle. devide the circle into 5 parts. color in 3 of the parts.
Now, draw 4 more of these.
Now, count the pieces.
Answer:1/2,-3/2,-3/8
Step-by-step explanation:
Number 14 is 61 and Number 16 is 36..,.
1 and 8 are because they are alternate exterior angles
