F(x) = = -x + 9
g(x) = x2 - 6x + 9
What is the value of g(f(0))

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

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

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