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

`f(g(x)) =  5x^(2)   + 10x+ 5`

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`