Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

What is the inverse of [tex]$f(x)=\frac{1}{3} x+2$[/tex]?

A. [tex]h(x)=\frac{1}{3} x+2[/tex]

B. [tex]h(x)=\frac{1}{3} x-2[/tex]

C. [tex]h(x)=3x-2[/tex]

D. [tex]h(x)=3(x-2)[/tex]

Sagot :

GinnyAnswer
To find the inverse of the function [tex]\( f(x) = \frac{1}{3} x + 2 \)[/tex], follow these steps:

1. Set [tex]\( y = f(x) \)[/tex]:
[tex]\[ y = \frac{1}{3} x + 2 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = \frac{1}{3} y + 2 \][/tex]

3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x = \frac{1}{3} y + 2 \][/tex]
Multiply both sides by 3 to clear the fraction:
[tex]\[ 3x = y + 6 \][/tex]
Subtract 6 from both sides to isolate [tex]\( y \)[/tex]:
[tex]\[ y = 3x - 6 \][/tex]

4. Thus, the inverse function is:
[tex]\[ h(x) = 3x - 6 \][/tex]

So, the correct inverse function is [tex]\( h(x) = 3x - 6 \)[/tex].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.