F (X) = x² - 2x and 6(x) = 3x+1 A) Find F(g(-4))
B) Find F(g(x)) simply
C) find g^-1 (x)

See bolded below

Step-by-step explanation:

With the given f(x) and g(x) given, we can directly plug them in to solve. The inverse is to replace the y with x and x with y, then solve for y.

A. f(g(-4))=143

g(-4)=3(-4)+1

g(-4)=-12+1

g(-4)=-11

With g(-4), we plug that into f(x) to find f(g(-4)).

f(-11)=(-11)²-2(-11)

f(-11)=121+22

f(-11)=143

B. 9x²-1

(3x+1)²-2(3x+1)

(9x²+6x+1)-6x-2

9x²-1

C. g⁻¹(x)=(x-1)/3

x=3y+1

x-1=3y

(x-1)/3=y

1 3 5

step-by-step explanation:

i took the test: )

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;