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!

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: