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Paraphin [41]
3 years ago
14

*20 POINTS PLEASE HELP ME!!!!!!!!*

Mathematics
1 answer:
egoroff_w [7]3 years ago
5 0

Answer:

helloooooooooooooooooooo

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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
F(x) = 3x + 1 and f ^-1=x-1/(over)3<br> then f -(7) =
nignag [31]
Answer and work in picture:

4 0
3 years ago
The total cost after tax to repair Kimber's cracked phone screen is represented by 0.04(30h) + 30h, where h represents the numbe
PSYCHO15rus [73]

In this equation there are few key numbers, thankfully XD, so it does not take too long to figure out that the 0.04 is clearly a tax on the repairs as 30h is representing the hours spent repairing Kimber's phone.

6 0
3 years ago
The large piston in a hydraulic lift has an area of 2m^2. What force must be applied to the small piston with an area of .2m^2 i
Helen [10]

Answer:

147,000N

Step-by-step explanation:

A1= 2m^2

A2= 0.2m^2

F2= 14,700N

Required

F1, the applied force

Applying the formula

F1/A1= F2/A2

substute

F1/2=14700/0.2

2*14700= F1*0.2

29400= F1*0.2

F1= 29400/0.2

F1=147,000N

Hence, the applied force is 147,000N

3 0
3 years ago
What property does the following equation show? 5+7+9=7+5+9<br>​
dsp73

Answer: it’s commutative property.

Step-by-step explanation: commutative property is when you switch numbers but the answer still stays the same. Hope this helped!

8 0
3 years ago
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