Question

F(x) = x2 + 1 and g(x) = x + 1 Which of the following best represents
f(g(x)) ?

Answer 1

Answer:
`f(g(x)) = x^2+2x+2`

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Work Shown:

`f(x) = x^2 + 1\\\\f(x) = ( x )^2 + 1\\\\f(g(x)) = ( g(x) )^2 + 1 \ \text{ replace every x with g(x)}\\\\f(g(x)) = ( x+1 )^2 + 1 \ \text{ plug in } g(x) = x+1\\\\f(g(x)) = ( x+1 )( x+1 ) + 1\\\\f(g(x)) = x^2+2x+1 + 1 \ \text{ use FOIL rule}\\\\f(g(x)) = x^2+2x+2\\\\`

Answer 2

Explanation:

Since you haven't given us any choices, I will just give an answer. You can match it.

f(g(x) = (g(x))^2 + 1

That means that wherever you see an x in f(x) you put g(x) in on the right.

f(g(x)) = (x + 1)^2 + 1

f(g(x)) = x^2 + 2x + 1 + 1

f(g(x)) = x^2 + 2x + 2