f(x)=2x+5 g(x)x2-25
1. show that gf(x)=4x2 + 20x
2. solve gf(x)=g(7)
could you please explain how you got the answer, thanks.
f(x) = 2x + 5
and
g(x) = x2 - 25
So to find g( f(x) ), replace every x in g(x) with f(x) .
g( f(x) ) = (2x + 5)2 - 25
g( f(x) ) = (2x + 5)(2x + 5) - 25
g( f(x) ) = 4x2 + 10x + 10x + 25 - 25
g( f(x) ) = 4x2 + 20x
If g( f(x) ) = g( 7 ) , then that means f(x) must equal 7.
f(x) = 7
2x + 5 = 7
2x = 7 - 5
2x = 2
x = 1
