Question 932963
2. {{{f(x)= sqrt(x-2)+5}}} ...I guess you have this (you didn't tell what is under sqrt exactly)

a. Find the inverse of f(x). Show the process.

{{{f(x)= sqrt(x-2)+5}}}...{{{f(x)=y}}}

{{{y= sqrt(x-2)+5}}}...swap {{{x}}} and {{{y}}}

{{{x= sqrt(y-2)+5}}}...solve for {{{y}}}

{{{x-5= sqrt(y-2)}}}...raise both sides to the power of {{{2}}}

{{{(x-5)^2= (sqrt(y-2))^2}}}

{{{x^2-10x+25= y-2}}}

{{{x^2-10x+25+2= y}}}

{{{y=x^2-10x+27}}}

so, inverse is {{{f^-1(x)=x^2-10x+27}}}

b. Find the domain of f -1.

{{{f^-1(x)=x^2-10x+27}}}

the domain: all real numbers

({{{-infinity}}},{{{infinity}}})

c. Graph f and f -1 on the same axes. What relationship do you see between the two graphs?

{{{ graph( 600, 600, -10, 10, -10, 30,sqrt(x-2)+5, x^2-10x+27) }}}


they intersect in two points