Find the inverse when f(x)=3x^2-3x-2

The inverse of f(x) is (x) =  ± +

Step-by-step explanation:

To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where

∵ f(x) = 3x² - 3x - 2

→ Compare it with the 1st form above to find a and b

∴ a = 3 and b = -3

→ Use the rule of h to find it

∵ h = = =

∴ h =  

→ Substitute x by the value of h in f to find k

∵ k = 3( )² - 3( ) - 2

∴ k =

→ Substitute the values of a, h, and k in the vertex form above

∵ f(x) = 3(x -  )² +

∴ f(x) = 3(x -  )² -

Now let us find the inverse of f(x)

∵ f(x) = y

∴ y = 3(x -  )² -

→ Switch x and y

∵ x = 3(y -  )² -

→ Add to both sides

∴ x + = 3(y - )²

→ Divide both sides by 3

∵ = (y - )²

→ Take √ for both sides

∴ ± = y -

→ Add   to both sides

∴ ± + = y

→ Replace y by (x)

∴ (x) =  ± +

∴ The inverse of f(x) is (x) =  ± +

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;