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!
Answer:
40.8
Step-by-step explanation:
Answer:
2,040
Step-by-step explanation:
24
×85=
5×4=20 carry the 2 about the 2 in 24
5×2=10+ the 2 you carried =120
bring a 0 down under the 0 in 120 cross out the 5
now do 8×4=32 carry the 3 above the two in 24 now
8×2=16+ the 3 carried=19
1120+1920=2,040
tye findamental theorem of calculs is cognitive
