Question 1076491
 If {{{f(g(x)) = 4x^2-8x}}} and {{{f(x) = x^2 -4}}} , then {{{g(x)}}} = ? 

to find {{{g(x)}}};

{{{f(g(x)) = 4x^2-8x}}},

from {{{f(x)}}};

{{{(g(x))^2 -4 = 4x^2 -8x}}}

{{{(g(x))^2 = 4x^2 -8x+4}}}

{{{(g(x))^2 = 4(x^2 -2x+1)}}}

{{{(g(x))^2 = 4(x-1)^2}}}

{{{g(x) = highlight(2(x-1))}}} or {{{g(x) = highlight(-2(x-1))}}}


check: if {{{f(x) = x^2 - 4}}} and {{{g(x) = 2(x-1)}}}

{{{f(g(x)) =f(2(x-1))= ( 2(x-1))^2 - 4= 4(x-1)^2 - 4=4(x^2 -2x+1)- 4=4x^2 -8x+4- 4=4x^2 -8x}}}
or

{{{f(g(x)) =f(-2(x-1))= ( -2(x-1))^2 - 4= 4(x-1)^2 - 4=4(x^2 -2x+1)- 4=4x^2 -8x+4- 4=4x^2 -8x}}}