How do you find the inverse of #f(x)=sqrtx# and graph both f and #f^-1#?

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Answer 1 · 2018-01-20T12:34:56

See the answer below.

To find the inverse function #f^-1(y)# of #f(x)=sqrt(x)#, we need to express #x# in terms of #y#, and then substitute #y# into #x#.

#f(x)=sqrt(x)#

#y=sqrt(x)#

#y^2=(sqrt(x))^2#

#y^2=x#

#:.f^-1(y)=y^2#

#:.f^-1(x)=x^2#

Here is the graph for #f(x)=sqrt(x)#:
graph{sqrt(x) [-10, 10, -5, 5]}

Here is the graph for #f^-1(x)=x^2#:

graph{x^2 [-10, 10, -5, 5]}