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kicyunya [14]
3 years ago
8

True or false: for any function, x=f^-1(y), then y=f(x)

Mathematics
2 answers:
GuDViN [60]3 years ago
8 0

Answer:

The given statement is false.                      

Step-by-step explanation:

Given :  For any function, x=f^{-1}(y) then y=f(x)

To find : The above statement is true or false?

Solution :

In the above statement the condition x=f^{-1}(y) then y=f(x) is valid for some function not for all.

Which means the statement is not true.

Taking a contrary example,

A trigonometric function  

The functiony=\sin x is one-one and onto in the domain[-\frac{\pi}{2},\frac{\pi}{2}]

Thus, its inverse exists in [-\frac{\pi}{2},\frac{\pi}{2}]

i.e., \text{In }[-\frac{\pi}{2},\frac{\pi}{2}],\ y=\sin x \Rightarrow\ x=\sin^{-1}(y).

It depends on the domain for the given statement to be true.

Therefore, The given statement is false.                                                                    

kozerog [31]3 years ago
6 0

YES

We can work out the inverse using Algebra. Put "y" for "f(x)" and solve for x:

<span><span>The function: f(x)=2x+3
</span><span>Put "y" for "f(x)": y=2x+3
</span><span>Subtract 3 from both sides:
 y-3=2x
</span><span>Divide both sides by 2:
 (y-3)/2=x
</span><span>Swap sides: x=(y-3)/2</span><span>  
   </span><span><span>Solution (put "f-1(y)" for "x") :</span> <span>f-1(y)</span>=(y-3)/2</span></span>


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Step-by-step explanation:

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Part 3: Complete the following metric conversions. Make sure to show all work to receive credit! You may
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Answer:

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Step-by-step explanation:

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1 mg = 0.001 g

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(104 km * 1000 m) / 1 km = 104,000 m

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6 0
3 years ago
Lisa an experienced shipping​ clerk, can fill a certain order in 7 hours. ​bill, a new​ clerk, needs
OLga [1]

Answer:

3.73 hours

Explanation:

In 1 hour, Lisa does 1/7th of the order while Bill does 1/8th of the order in an hour. To find out how long it will take them to fill the order, we have to:

Step 1:

Add the rate of both Lisa and Bill together

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Step 2:

Since both denominators of the fractions are different, you have to find the least common multiple of 7 and 8

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Step 3:

Then, you have to multiply the numerator of 1/7 with 8 and the numerator of 1/8 with 7.

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The fractions would now have equal denominators:

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Step 4:

Now, you can add them together

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Step 5:

15/56 is not the final answer as it is the RATE of them working together. To find how long it will take them total to complete the order, you must divide 56 with 15.

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which is 3.73 hours in decimal form (rounded).

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