The domain of the function exists for when x ≤ 2 while the range exists for the value of y >0
For f⁻¹(x), the domain and the range exists on all real values
Given the expression
f(x)=√−2x+4
Get the inverse of the function f⁻¹(x)
ley u = f(x)
y = √−2x+4
Replace x as y
x = √−2y+4
Make y the subject of the formula
x² = -2y + 4
-2y = x²-4
y = (x²-4)/-2
Hence f⁻¹(x)= (x²-4)/-2
For f(x), the domain of the function exists for when x ≤ 2 while the range exists for the value of y >0
For f⁻¹(x), the domain and the range exists on all real values
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