They want you to find the composite function and they evaluate it at a give value for x...first the composite function...
f(g(x))=(x-1.5)^2+3(x-1.5)+6
f(g(x))=x^2-3x+2.25+3x-4.5+6
f(g(x))=x^2+3.75, this is the completed composition function...now:
f(g(1)=1+3.75=4.75
Area = b × h
= 10 × 17
= 170 meters2
Answer:
You know that if f(x) = 1/(x²+1) then F(x)=arctan(x).
What is arctan(x) function? It is inverse function of tan(x) in tge range (-π/2, π/2).
So if tan(x) = y then x = arctan(y)
therefore arctan(-1) = -π/4 because tan(-π/4)=-1 and arctan(1)=π/4 because tan(π/4) = 1.
In conclusion:
integral (dx/(x²+1)) from -1 to 1 =
= F(1) - F(-1) = arctan(1) - arctan(-1) =
=π/4-(-π/4)=π/4+π/4 = π/2.
answer B is correct
-9
Step-by-step explanation:
1/5^9=5^1
5^-9=5^1
-9=1
therefore the answer is -9
