**f(x)=2x-3 and g(x)=√4x+3**

**find (f ° g)(x)**

**Find the domain of (f ° g)(x)**

**Find (g ° f)(x)**

**g(x)=√4x+3**

**f(x)=2x-3**

**Find the domain of (g ° f)(x)**

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??

Tutors, sign in to answer this question.

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

(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.

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)**

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

(g ° f)(x)=√(4(2x-3)+3)

Let's simplify.

(g ° f)(x)=√8x-12+3

(g ° f)(x)=√8x-9

We cannot square root a negative number.

Therefore,

8x-9≥0

8x≥9

x≥9/8

The domain is...

(9/8, ∞)

Gabrielle P. | I love to teach just about everythingI love to teach just about everything

(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

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Milton Rafael N.

Math, ACT, GRE, SAT, ASVAB,TEAS, Engineering, Spanish & more

$8.75 per 15 min

View Profile >

Samantha J.

Middle and High School Tutor with 3-4 Years Experience

$7.50 per 15 min

View Profile >

Tomas G.

Experienced Tutor for more than 10 years

$7.50 per 15 min

View Profile >