IDNLearn.com makes it easy to find precise answers to your specific questions. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

What is the inverse of the function [tex]$f(x)=\frac{1}{4}x-12$[/tex]?

A. [tex]h(x)=48x-4[/tex]

B. [tex]h(x)=48x+4[/tex]

C. [tex]h(x)=4x-48[/tex]

D. [tex]h(x)=4x+48[/tex]


Sagot :

To find the inverse of the function [tex]\( f(x) = \frac{1}{4}x - 12 \)[/tex], follow these steps:

1. Rewrite the function as [tex]\( y = \frac{1}{4}x - 12 \)[/tex]:
[tex]\[ y = \frac{1}{4}x - 12 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[ x = \frac{1}{4}y - 12 \][/tex]

3. Solve the equation for [tex]\( y \)[/tex]:
- First, add 12 to both sides:
[tex]\[ x + 12 = \frac{1}{4}y \][/tex]

- Next, multiply both sides by 4 to isolate [tex]\( y \)[/tex]:
[tex]\[ 4(x + 12) = y \][/tex]
[tex]\[ y = 4x + 48 \][/tex]

4. Therefore, the inverse function [tex]\( h(x) \)[/tex] is:
[tex]\[ h(x) = 4x + 48 \][/tex]

Given the options:
- [tex]\( h(x) = 48x - 4 \)[/tex]
- [tex]\( h(x) = 48x + 4 \)[/tex]
- [tex]\( h(x) = 4x - 48 \)[/tex]
- [tex]\( h(x) = 4x + 48 \)[/tex]

The correct inverse function is:
[tex]\[ h(x) = 4x + 48 \][/tex]

So the correct option is:
[tex]\[ h(x)=4x+48 \][/tex]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.