Question

HELP OFFERING 50 points!!

Answer 1

Answer:

$f(g(x)) = 5x^{2} + 10x+ 5$

Step-by-step explanation:

Here, the given functions are:

$f(x) = 5x^2\\g(x) = x+1$

Now, (fg)(x)  = f (g(x))

f(g(x))= f (x+1)

$\implies f(x+1) = 5(x+1)^2$

By ALGEBRAIC IDENTITY:

$(a+b)^2 = a^2 + b^2 + 2ab\implies (x+1)^2 = x^{2} + 1 + 2x$

So, $5(x+1)^2 = 5(x^{2} + 2x + 1) = 5x^{2} + 10x+ 5$

Hence, $f(g(x)) = 5x^{2} + 10x+ 5$