Question

HELP OFFERING 50 points!!

F(x) = 5x ^ 2 and g(x) = x + 1 find (fg)(x)

A 5x^3 +1
B 5x^4+5x^3
C 5x^4+1
D 6x^3

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, $f(g(x)) =  5x^{2}   + 10x+ 5$