How does a domain restriction placed on a non-invertible function affect its inverse?
Drag a function or an interval into each box to correctly complete the statement.
When the domain of the non-invertible function f(x)=(x+1)^2 − 3 is [−1,∞), the inverse of the function is f^−1(x) = √x+3 -1, and the domain of the inverse function is [3, ∞).
my answers are bolded. they are correct?? thx !!
+128474 Note that in the origial function f(-1) = -3 .....the point (-1,-3) is on the graph of the original
So....the point (-3, -1) is on the inverse
Find the inverse
y = ( x + 1)^2 - 3
y + 3 = ( x + 1)^2 take the positive root
sqrt ( y + 3) = x + 1 subtact 1 from both sides
sqrt (y+ 3) - 1 = x "swap" x and y
y = sqrt (x + 3) - 1 = the inverse
Note that (-3,-1) is on the graph
And the domain is [ -3, inf )
See the graph here : https://www.desmos.com/calculator/kjrdf25ehj
