Help! Let f(x) be a function with domain [-3, ∞ ) and range (- ∞ , 2). If g(x) = f^-1 (x) (aka. g(x) is the inverse of f(x)), then what is the domain of g(x+4)-7 ?

1 Answer
Mar 26, 2018

Answer:

#[-10,oo)# Range
#(-oo,6)# Domain

Explanation:

First of with inverse functions the domain and range switch so as #g(x)=f(x)^-1# the domain is #(-oo,2)# and the range #[-3,oo)#

We know that the whole of function #g(x)# has been shifted 7 downards so the range changes by the same amount #[-10,oo)#

As #g(x)# has moved 4 to the RHS so the domain moves 4 to the right #(-oo,6)#