If #f(x) = sqrt(3x+5)# and #g(x) = sqrt(25x-16)#, what is #(fg)(x)#?

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Answer 1 · 2016-06-01T00:17:04

Arithmetic with functions is much the same as arithmetic with natural numbers.

#(fg)(x) = (f xx g)(x)#

#= sqrt(3x + 5) xx sqrt(25x - 16)#

#= sqrt((3x + 5)(25x - 16))#

#=sqrt(75x^2 + 125x - 48x - 80)#

#= sqrt(75x^2 + 77x - 80)#

Therefore #(fg)(x) = sqrt(75x^2 + 77x - 80)#.

Hopefully this helps!