How do you find #(fog)(10)# given #f(x)=-9x-9# and #g(x)=sqrt(x-9)#?

1 Answer
Apr 12, 2017

#color(red)(-18)#

Explanation:

#(fog)(x)# basically means #f(g(x))# #i.e.# a function obtained by substituting #g(x)# in place of #x# in #f(x)#.

hence in this case,

#(fog)(x) = f(g(x)) = -9*g(x) - 9#
#= -9*sqrt(x-9) - 9 = -9sqrt(x-9)-9#

#therefore# #(fog)(10) = f(g(10)) = -9sqrt(10-9)-9#
#= -9*1-9 = -9-9 = color(red)(-18)#

Another way to do it would have been to first find #g(10)# ant then substitute the value obtained into #f(x)#.
#therefore# #g(10) = sqrt(10-9) = color(red)1#
#therefore# #f(1) = -9*1-9 = 9-9 = color(red)(-18)#