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shtirl
2 months ago
10

Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-fifth x minus four-fifths? f Superscript n

egative 1 Baseline (x) = negative one-fifth x + four-fifths
Mathematics
2 answers:
Zina [12.3K]2 months ago
7 0

Answer:

The solution is "-5x-4"

Step-by-step explanation:

Given:

\bold{f^{-1} (x)=(-\frac{1x}{5}-\frac{4}{5})}

resolve the provided equation:

\to f^{-1}(x)= \frac{-x-4}{5}\\\\\to f^{-1}(x)= -\frac{x+4}{5}\\

Let

y= f^{-1} x= -(\frac{x+4}{5})\\\\

find the inverse of the function above:

\to x= -(\frac{y+4}{5})\\\\\to 5x= -(y+4)\\\\\to 5x= -y-4\\\\\to\boxed {y=-5x-4}\\\\

lawyer [12.5K]2 months ago
3 0
The inverse of the function is g (x)=-5x-4. To find this, we start with the given function: f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}. Let us denote y=f^{-1}(x) for further calculations. Substituting will yield the equation: y=\frac{-x-4}{5}. To proceed with determining the inverse, exchange x and y in the equation. The result of this substitution leads to: x=\frac{-y-4}{5}, then continues until we derive the value for y as: g (x)=-5x-4. This gives us the inverse function as g (x)=-5x-4.
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Answer:

0.5r

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If Jerry completed his journey in half the duration that Macy did, it implies Macy's time was twice as lengthy. Assuming Jerry’s speed is r, Macy’s speed would therefore be 0.5r, indicating she travels at half Jerry's pace and takes twice as long to cover the distance.

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1 month ago
A recipe for salsa uses 65% tomatoes. If a batch contains 5.2 cups of tomatoes, how large is the batch of salsa.
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The salsa consists of 65% tomatoes, which amounts to 5.2 cups.

Let’s denote the total salsa as "x" cups, representing 100%. Given that 5.2 cups makes up 65%, we have:

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1 month ago
Which shows the factored form of x2 – 12x – 45?
AnnZ [12381]
Hello!

(x+a)·(x+b) equals x²+xa+xb+ab which simplifies to x²-12x-45

x² equals x²
xa+xb can be expressed as (a+b)x = -12x thus, (a+b) = -12
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Under what conditions do (a+b) equal -12 and ab equal -45?

+3-15 results in -12 while (+3)(-15) gives -45
-3-15 yields -18 and (-3)(-15) results in +45
+3+15 produces +18 and (+3)(+15) also equal to +45
-3+15 equals +12 and (-3+15) results in -45

Conclusion:

(x+3)(x-15) 



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Answer:

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