Question

The functions f and g are defined as follows f(x)=5x+3/6x+7 and g(x)= square root sign x^2-4x

find f(6/x) and g(x-4)

Answer 1

f(x)=5x+3/6x+7

This means that f(6/x) = [5(6/x)+3] / [6(6/x)+7] = [ 30/x +3 ] / [36/x +7]

If we assume x≠0 , f(6/x) = [30 +3x]/ [36 + 7x]

g(x)=√ [ x^2-4x ]

g(x-4) = √ [ (x-4)^2-4(x-4) ] = √ [ x² -8x +16 -4x +16 ] = √ [ x^2-12x +32]