Answer:
[tex] f(g(x)) = 5x^{2} + 10x+ 5[/tex]
Step-by-step explanation:
Here, the given functions are:
[tex]f(x) = 5x^2\\g(x) = x+1[/tex]
Now, (fg)(x) = f (g(x))
f(g(x))= f (x+1)
[tex]\implies f(x+1) = 5(x+1)^2[/tex]
By ALGEBRAIC IDENTITY:
[tex](a+b)^2 = a^2 + b^2 + 2ab\implies (x+1)^2 = x^{2} + 1 + 2x[/tex]
So, [tex]5(x+1)^2 = 5(x^{2} + 2x + 1) = 5x^{2} + 10x+ 5[/tex]
Hence, [tex] f(g(x)) = 5x^{2} + 10x+ 5[/tex]
