Math  /  Algebra

QuestionQuestion 1-2 Write an equation for the inverse of g(x)=3x8g(x)=3 x-8. g1(x)=8x3g^{-1}(x)=8 x-3 g1(x)=13x+8g^{-1}(x)=\frac{1}{3} x+8 g1(x)=x+83g^{-1}(x)=\frac{x+8}{3} g1(x)=x+83g^{-1}(x)=x+\frac{8}{3}

Studdy Solution

STEP 1

1. We are given a linear function g(x)=3x8 g(x) = 3x - 8 .
2. We need to find the inverse function g1(x) g^{-1}(x) .
3. The inverse function will "undo" the operation of the original function.

STEP 2

1. Set g(x)=y g(x) = y and solve for x x in terms of y y .
2. Express the inverse function g1(x) g^{-1}(x) using the result from step 1.

STEP 3

Set g(x)=y g(x) = y , so we have:
y=3x8 y = 3x - 8
Solve for x x in terms of y y .
Add 8 to both sides to isolate the term with x x :
y+8=3x y + 8 = 3x

STEP 4

Divide both sides by 3 to solve for x x :
x=y+83 x = \frac{y + 8}{3}

STEP 5

Now express the inverse function g1(x) g^{-1}(x) by replacing y y with x x :
g1(x)=x+83 g^{-1}(x) = \frac{x + 8}{3}
This is the equation for the inverse of g(x) g(x) .
The correct answer is:
g1(x)=x+83 g^{-1}(x) = \frac{x + 8}{3}

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