Type the composition (fog)(x) of the given functions:

Question

f(x) = x² + 2x − 6 and g(x) = x + 5.

Answer 1

Hi there! I'd love to help you out...

When working with compositions, I like to change their form a little bit instead of having it in the "fog" form:

(fog)(x) = f( g(x) )

This means we can go through our "f" function and wherever there is an "x" we will plug in our "g" function"

f( g(x) ) = (x + 5)² + 2(x + 5) - 6

Now we just simplify:

f( g(x) ) = (x + 5)(x + 5) + 2x + 10 -6

x² + 5x + 5x + 25 + 2x + 10 -6

f( g(x) =x² + 12x + 29

And there you have it! I hope this explanation was thorough and answered all of your questions. If you have any additional questions, please don't hesitate to reach out. Learn on! :)

Answer 2

Lucy, composition of functions is straightforward, though a bit tedious.

The problem wants f(g(x)).

First, substitute “g(x)” in place of “x” into the definition of f(x):

f(g(x)) = ( g(x))² + 2g(x) -6

Second, substitute the formula for g(x) for each instance of g(x):

f(g(x)) = (x+5)² + 2(x+5) - 6

Finally, multiply out and collect terms. I’m sure you know how.

Answer 3

f(x) = x² + 2x − 6 and g(x) = x + 5

(fοg)(x) = g(x)² + 2g(x) - 6

(fοg)(x) = (x+5)² + 2(x+5) - 6

Can you finish it from here?