Answer: 36
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Step-by-step explanation:
f(x) = -x+9
f(0) = -0+9 .... replace x with 0
f(0) = 9
We will replace f(0) with 9 in the g(x) function. In other words, we plug in x = 9 into the g(x) function
This is because g( f(0) ) = g( 9 )
g(x) = x^2 - 6x + 9
g(9) = 9^2 - 6*9 + 9 ... replace x with 9
g(9) = 81 - 54 + 9
g(9) = 36
Therefore, g(f(0)) = g(9) = 36 or simply g(f(0)) = 36
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Another method is to compute g(f(x)) algebraically first
g(x) = x^2 - 6x + 9
g(f(x)) = ( f(x) )^2 - 6*( f(x) ) + 9 .... replace every x with f(x)
g(f(x)) = ( -x+9 )^2 - 6*( -x+9 ) + 9 .... replace f(x) with -x+9
g(f(x)) = x^2 - 18x + 81 + 6x - 54 + 9
g(f(x)) = x^2 - 12x + 36
then we plug in x = 0
g(f(x)) = x^2 - 12x + 36
g(f(0)) = 0^2 - 12*0 + 36 ... replace x with 0
g(f(0)) = 36