f(x)=2x+5 g(x)x^{2}-25

1. show that gf(x)=4x^{2} + 20x

2. solve gf(x)=g(7)

could you please explain how you got the answer, thanks.

f(x) = 2x + 5

and

g(x) = x^{2 }- 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) ) = 4x^{2} + 10x + 10x + 25 - 25

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