Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine the inverse of the function [tex]\( f(x) = -5x - 4 \)[/tex], we need to follow several steps to solve for the inverse function. Let's do this in a detailed, step-by-step manner.
1. Start with the original function [tex]\( y = -5x - 4 \)[/tex]:
[tex]\[ y = -5x - 4 \][/tex]
2. Switch [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to begin solving for the inverse:
[tex]\[ x = -5y - 4 \][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
- First, add 4 to both sides to begin isolating [tex]\( y \)[/tex]:
[tex]\[ x + 4 = -5y \][/tex]
- Next, divide both sides by [tex]\(-5\)[/tex]:
[tex]\[ y = \frac{-(x + 4)}{5} \][/tex]
4. Simplify the expression for [tex]\( y \)[/tex]:
[tex]\[ y = -\frac{x + 4}{5} \][/tex]
[tex]\[ y = -\frac{1}{5}x - \frac{4}{5} \][/tex]
So, the inverse function is:
[tex]\[ f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} \][/tex]
Now we need to match this result with one of the given choices:
1. [tex]\( f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} \)[/tex]
2. [tex]\( f^{-1}(x) = -\frac{1}{5}x + \frac{4}{5} \)[/tex]
3. [tex]\( f^{-1}(x) = -4x + 5 \)[/tex]
4. [tex]\( f^{-1}(x) = 4x + 4 \)[/tex]
Clearly, the correct option is:
[tex]\[ f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} \][/tex]
Therefore, the inverse function of [tex]\( f(x) = -5x - 4 \)[/tex] is [tex]\( -\frac{1}{5}x - \frac{4}{5} \)[/tex], which corresponds to:
[tex]\[ \boxed{1} \][/tex]
1. Start with the original function [tex]\( y = -5x - 4 \)[/tex]:
[tex]\[ y = -5x - 4 \][/tex]
2. Switch [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to begin solving for the inverse:
[tex]\[ x = -5y - 4 \][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
- First, add 4 to both sides to begin isolating [tex]\( y \)[/tex]:
[tex]\[ x + 4 = -5y \][/tex]
- Next, divide both sides by [tex]\(-5\)[/tex]:
[tex]\[ y = \frac{-(x + 4)}{5} \][/tex]
4. Simplify the expression for [tex]\( y \)[/tex]:
[tex]\[ y = -\frac{x + 4}{5} \][/tex]
[tex]\[ y = -\frac{1}{5}x - \frac{4}{5} \][/tex]
So, the inverse function is:
[tex]\[ f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} \][/tex]
Now we need to match this result with one of the given choices:
1. [tex]\( f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} \)[/tex]
2. [tex]\( f^{-1}(x) = -\frac{1}{5}x + \frac{4}{5} \)[/tex]
3. [tex]\( f^{-1}(x) = -4x + 5 \)[/tex]
4. [tex]\( f^{-1}(x) = 4x + 4 \)[/tex]
Clearly, the correct option is:
[tex]\[ f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} \][/tex]
Therefore, the inverse function of [tex]\( f(x) = -5x - 4 \)[/tex] is [tex]\( -\frac{1}{5}x - \frac{4}{5} \)[/tex], which corresponds to:
[tex]\[ \boxed{1} \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.