The best answer (and only correct answer) among the answer choices given is: ________________________________________________ [C]: y⁻¹ = (x+6) / 3 . _________________________________________________ Explanation: __________________________________________________ Given the original function: y = 3x - 6 ; _________________________________________________ To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite: _________________________________________________ x = 3y <span>− 6 ;
Now, rewrite in "slope-intercept form" ; or y = mx + b ; that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only); then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope"; and "b" refers to the 'y-intercept". _____________________________________ So,we have the inverse function: ____ </span>_________________________________________________ x = 3y − 6 ; we want to write in slope-intercept form; __________________________________________________ Add "6" to each side of the equation: __________________________________ x + 6 = 3y − 6 + 6 ; __________________________________ x + 6 = 3y ; ________________________ ↔ Rewrite as: 3y = x + 6 ; ________________________________________ Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form: ______________________________ 3y / 3 = (x + 6) / 3 ; ______________________________ to get: ______________________________ y = (x + 6) / 3 ; _________________________________ y = (x/3) + (6/3) ; ____________________________________ y = (x/3 ) + 2 ; ___________________________________ or; write as: y = (1/3)x + 2 ; ________________________________________ Now, let us examine the answer choices given: __________________________________________ Note that all the answer choices begin with "y-1" ; (except "answer choice: [B]" , which begins with "x-1"). This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1". Rather, it mean y⁻¹ or x⁻¹ as notation for the "inverse" (not to be confused with the exponent notation. The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system. __________________________________________________ That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as: _____________________________________ y⁻¹ = (x + 6) / 3 ; _________________________________ y⁻¹ = (x/3) + (6/3) ; ____________________________________ y⁻¹ = (x/3 ) + 2 ; ___________________________________ or; write as: y⁻¹ = (1/3)x + 2 ___________________________________ That being said: _________________________________________ The best answer (and only correct answer) among the answer choices given is: Answer choice: [C]: y⁻¹ = (x+6) / 3 . ____________________________________________________
