Question

SOS PLZ HELP ME!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Answer:

$4x^{2}+14x+12$

Step-by-step explanation:

A way of thinking about this is x being an input and f(x) or g(x) being an output.

So, they want you to find g(f(x)), so that means they want the output of f(x) as the input for g(x). To clarify this, let's look at their functions:

$f(x) = 2x + 1\\ g(x) = x^{2} + 5x + 10$

If we want the output of f(x) to be the input of g(x) we would need to substitute the x in the g(x) function with the actual f(x) function itself.

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

As you can see the x's in g(x) were replaced with the f(x) function. At this point we just do algebra:

Foil the first term:

$(4x^{2} + 4x + 1) + 5(2x+1) + 10$

Distribute the second term:

$4x^{2} + 4x+1 + 10x + 1 + 10$

Condense like terms:

$4x^{2}+14x+12$