Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Complete the inverse function for the function given below.

[tex]
\begin{array}{c}
f(x) = 2x - 4 \\
f^{-1}(x) = \square x + \square \\
\end{array}
\]

Sagot :

GinnyAnswer
To find the inverse function of [tex]\( f(x) = 2x - 4 \)[/tex], we follow these steps:

1. Write down the function:
[tex]\[ y = 2x - 4 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse:
[tex]\[ x = 2y - 4 \][/tex]

3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x + 4 = 2y \][/tex]
[tex]\[ y = \frac{x + 4}{2} \][/tex]

4. Express the result in the form [tex]\( f^{-1}(x) = ax + b \)[/tex]:
[tex]\[ f^{-1}(x) = \frac{1}{2}x + 2 \][/tex]

Therefore, the completed inverse function is:
[tex]\[ f^{-1}(x) = 0.5x + 2 \][/tex]

So, in the blanks:
[tex]\[ f^{-1}(x) = \boxed{0.5} x + \boxed{2} \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.