How do you find the inverse of # y =sqrt(x-4)#?

1 Answer
Alan P.
Dec 9, 2015

#x=y^2+4#
or if you wish to keep #y# as the dependent variable:
#y=x^2+4#

Explanation:

Method 1:
#y=sqrt(x-4)#

#rArr y^2 = x-4#

#rArr y^2+4 = x color(white)("XXx")orcolor(white)("XXX")x=y^2+4#

Method 2: (perhaps more complex but more technically accurate)
Let
#color(white)("XXX")f(x)=y#
and
#color(white)("XXX")barf (x)# be the inverse of #f(x)#

By definition of inverse:
#color(white)("XXX")f(barf(x)) = x#

But since
#color(white)("XXX")f(x) = sqrt(x-4)#
#rArr#
#color(white)("XXX")f(barf(x))= sqrt(barf(x)-4)#

So
#color(white)("XXX")sqrt(barf(x)-4) = x#

#color(white)("XXX")barf(x)-4 = x^2#

#color(white)("XXX")barf(x)=x^2+4#

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