Consider the function h whose domain is the interval [-7, 7], with h defined on

Question

Consider the function h whose domain is the interval [-7, 7], with h defined on this domain by the formula h(x) = (7 + x)^2. Does h have an inverse? If so, find it, along with its domain and range. If not, explain why not. h^-1(y) = squareroot y - 7 with domain [0, Infinity) and range [-7, infinity). h^-1(y) = -squareroot y - 7 with domain [0, 196) and range [-infinity, 7). h^-1(y) = plusminus squareroot y - 7 with domain [0, infinity) and range [-infinity, infinity). h does not have an inverse because h is not one-to-one. h^-1(y) = squareroot y - 7 with domain [0, 196) and range [-7, 7).

Explanation / Answer

h(x) = ( 7 +x)^2

find inverse : plug x = h and h = x , solve for h:

x = (7 +h)^2

h^-1(x)= -7 +/- sqrtx

Inverse doe not exist as h(x) is not 1-1 function

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