f(x)=2x+3
g(x)=x²-5
a.(gof)(x)
b.(fog)(x)
c.(gof)(-2)![]()
g(x)=x²-5
a.(gof)(x)
b.(fog)(x)
c.(gof)(-2)
a :
[tex](gof)(x) = g(f(x)) \\ = {(2x + 3)}^{2} - 5 \\ =(2x + 3) \times (2x + 3) - 5 \\ = ( {4x}^{2} + 6x + 6x + 9) - 5 \\ = {4x}^{2} + 12x + 9 - 5 \\ = {4x}^{2} + 12x + 4[/tex]
b :
[tex](fog)(x) = f(g(x)) \\ = 2( {x}^{2} - 5) + 3 \\ = {2x}^{2} - 10 + 3 \\ = {2}^{2} - 7[/tex]
c :
[tex](gof)( - 2) = g(f( - 2) \\ = {4( - 2)}^{2} + 12( - 2) + 4 \\ = 4(4) + ( - 24) + 4 \\ = 16 + ( - 24) + 4 \\ = - 4[/tex]
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