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mars1129 [50]
2 years ago
8

Help This is for 6th grade math!

Mathematics
1 answer:
Svetlanka [38]2 years ago
3 0

Answer:

1.) -4

2.) 3

3.) 4

If you need a little extra help knowing what to do with these problems, you should draw a number line that includes negative and positive numbers. You can count along the number line. It's a good visual aid.

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Consider the function f(x)= 2/5x-4
Gre4nikov [31]

Answer: a) \frac{5}{2}x+10=f^{-1}(x)=g(x)

Step-by-step explanation:

Since we have given that

f(x)=\frac{2}{5}x-4

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

y=\frac{2}{5}x-4

Switching x to y , we get

x=\frac{2}{5}y-4

5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)

b) . Use composition to show that f(x) and g(x) are inverses of each other.

\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x

Similarly,

\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.


5 0
3 years ago
What multiplies to 30 but adds to -7
FinnZ [79.3K]

10 * 3

hope I helped :)

6 0
2 years ago
Read 2 more answers
A family eats at a restaurant . The bill is$ 42 dollars . The family leaves a tip and spends $ 49.77 dollars .
bagirrra123 [75]

Answer:

Since you didnt include an actual question im guessing you are looking for the tip amount which would be $ 7.77

Step-by-step explanation:

49.77-42=7.77

3 0
3 years ago
Read 2 more answers
The train travels 580 miles in 4 hours. The train travels at a constant rate. At this rate, how many hours will it take the trai
Mandarinka [93]

We set up the equation 580/4 = 725/x. Since we know these are proportional, we can cross-multiply and solve to get x = 5.

8 0
2 years ago
What is the difference between 29035 and -36198
TiliK225 [7]
29035 is a positive and -36198 is a negative
4 0
3 years ago
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