Question

Find the inverse of the following function algebraically. Show all work. f(x)=-5√-4x+4+2

Answer 1

I will assume you meant
f(x) = -5√(-4x+4) + 2
or else they would have just added the 2 to the 4

y = -5√(-4x+4) + 2
= -10√(1-x) + 2 , I factored out √4 which is 2

inverse: interchange x and y variables
x = -10√1-y) + 2

solve this new equation for y:
10√(1-y) = 2 - x
square both sides:
100(1-y) = 4 - 4x + x^2
1-y = (4-4x + x^2)/100
y = 1 - (4 - 4x + x^2)/100
= (96 + 4x - x^2)/100

check:
pick any value for x, say x = 0
f(-3) = -5√4 + 2 = -8

put that into the inverse:
y = (96 - 32 - 64)/100 = 0

good chance that I am correct

Answer 2

should have noted that the original function is only valid for x ≤ 1

Answer 3

So the answer would be x = -10√1-y) + 2 or (96 + 4x - x^2)/100?