HELP functions

Question

f(x)=2x-3 and g(x)=√4x+3

 

find (f ° g)(x)

Find the domain of (f ° g)(x)

Find (g ° f)(x)

Find the domain of (g ° f)(x)

 

can someone lead me in the right direction on how to do these??

Answer 1

Hi Erica;

In the function of f(x), x is considered as x.

In the function of (f ° g)(x), x is considered as g(x).

This is about substitution.

f(x)=2x-3 and g(x)=√4x+3
find (f ° g)(x)

f(x)=2x-3

(f ° g)(x)=2(√4x+3)-3

I am assuming we are square-rooting 4x+3, not just 4x.  If not, please let me know.

Find the domain of (f ° g)(x)

As you already know, a square-rooted number must be equal to or greater than zero.

So...

4x+3≥0

Let's subtract 3 from both sides...

4x+3-3≥0-3

4x≥-3

Let's divide both sides by 4.

4x/4≥-3/4

x≥-3/4

This domain of this equation is -3/4 to infinity.

domain=(-3/4,∞)

 

In the equation of (g ° f)(x), x is considered as f(x)...
Find (g ° f)(x)

g(x)=√4x+3

As before, I am assuming that we are square-rooting 4x+3, not just 4x.  If not, please let me know.

f(x)=2x-3

(g ° f)(x)=√(4(2x-3)+3)

Let's simplify.

(g ° f)(x)=√8x-12+3

(g ° f)(x)=√8x-9

Find the domain of (g ° f)(x)

We cannot square root a negative number.

Therefore,

8x-9≥0

8x≥9

x≥9/8

The domain is...

(9/8, ∞)

Answer 2

(Fog) is f of g which means use g as your x value in your f(x) equation

 

same goes for (gof) use f(x) as your x value in the g(x) equation

 

your domain is every number that can possibly be the value of x