b Graph f and f 1 in the same rectangular coordinate system

?,

?(b) Graph f and f ^-1 in the same rectangular coordinate system.

?(c) Use interval notation to give the domain and the range of f and f ^-1

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Solution

f(x) = sqrt(x-7)

Domain : x- 7>=0

x>=7

So, inverse exists for this domain

y = sqrt(x-7)

Plug x= y and y = x , solve for y

x = sqrt(y-7)

x^2 +7 = y

y = x^2 +7

f^-1(x) = x^2 +7

Domain : [ 7 , inf)

Range : y >=0

[0 , inf )