Find f^1(x) for f(x)= -3x+2 and state whether or not it is a function.

a : f^1(x)= -1/3x +2/3 ; function

b : f^1(x)= 1/3x -2/3 ; not a function

c : f^1(x)= 1/3x +2/3 ; function

d : f^1(x)= -1/3x -2/3 ; function

A

Step-by-step explanation:

f^-1(x) is a common notation for the inverse of the function. An inverse of a function is a reflection over the line y=x. This results in the points (x,y) of the function becoming (y,x) for the inverse. Algebraically you find the inverse by switching the location of y and x in the equation of the function and solving.

y = -3x + 2

x = -3y + 2

x - 2 = -3y

-(x-2)/3 = y

-1/3x + 2/3 = y

The inverse of the function is a linear function because it follows the form y = mx+b for its equation. All lines are functions. The inverse is a function.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)