Given that f(x) = √(ax + 1) , with x ≥ -1/a and a > 0 and g(x) = (x+1)/x, with x ≠ 0.
if ( f~¹ • g~¹) (3) = -⅜ ,
find : a²+ 3a -3 !​

Step-by-step explanation:

first thing I assume by f~¹ you meant however

we want to find a²+3x-3 for the given condition. with the composite function condition we can do so

Finding the inverse of f(x):

substitute y for f(x):

interchange:

square both sides:

cancel 1 from both sides:

divide both sides by a:

substitute f^-1 for y:

finding the inverse of g(x):

substitute y for g(x)

interchange:

cross multiplication

cancel 1 from both sides

factor out y:

divide both sides by 1-x:

substitute g^-1 for y:

remember that

therefore we obtain:

since (f~¹•g~¹)(3)=-⅜ thus substitute:

simplify parentheses:

simplify square:

simplify substraction:

simplify complex fraction:

get rid of - sign:

divide both sides by 3:

cross multiplication:

divide both sides by 4:

as we want to find a²+3a-3 substitute the got value of a:

simplify square:

simplify multiplication:

simplify addition:

simplify substraction:

and we are done!

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all

6/20

step-by-step explanation: