Studdy AI Logo
Math

QuestionFind f(g(h(3)))f(g(h(3))) for f(x)=−2x3f(x)=-2 x^{3}, g(x)=3x−5g(x)=3 x-5, and h(x)=x−1h(x)=x-1. Options: −129-129, −54-54, −53-53, −2-2.

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x) is given by f(x)=−x3f(x)=- x^{3} . The function (x)(x) is given by g(x)=3x−5g(x)=3 x-5
3. The function h(x)h(x) asked to find the value of f(g(h(3)))f(g(h(3)))

STEP 2

First, we need to find the value of h()h(). We can do this by substituting x=x= into the function h(x)h(x).
h()=−1h() = -1

STEP 3

Calculate the value of h(3)h(3).
h(3)=3−1=2h(3) =3 -1 =2

STEP 4

Now that we have the value of h(3)h(3), we can find the value of g(h(3))g(h(3)). We do this by substituting x=h(3)x=h(3) into the function g(x)g(x).
g(h(3))=g(2)=3⋅2−g(h(3)) = g(2) =3 \cdot2 -

STEP 5

Calculate the value of g(h(3))g(h(3)).
g(h(3))=3⋅2−5=1g(h(3)) =3 \cdot2 -5 =1

STEP 6

Now that we have the value of g(h(3))g(h(3)), we can find the value of f(g(h(3)))f(g(h(3))). We do this by substituting x=g(h(3))x=g(h(3)) into the function f(x)f(x).
f(g(h(3)))=f(1)=−2⋅13f(g(h(3))) = f(1) = -2 \cdot1^{3}

STEP 7

Calculate the value of f(g(h(3)))f(g(h(3))).
f(g(h(3)))=−2⋅13=−2f(g(h(3))) = -2 \cdot1^{3} = -2So, f(g(h(3)))=−2f(g(h(3))) = -2.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord