24 runners were faster than Colby in a race. If 30% of the runners were faster than Colby, what was the total number of runners
2 answers:
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Answer:
No extraneous solution
Step-by-step explanation:
We have the logarithmic equation given by,
i.e.
i.e.
i.e.
i.e.
i.e.
i.e.
So, the solution of the given equation is x=4.
Now, as we domain of square root function is x > 0 and also, the domain of logarithmic function is .
Therefore, the domain of the given function is x > 0.
We know that the extraneous solution is the solution which does not belong to the domain.
But as x=4 belongs to the domain x > 0.
Thus, x = 4 is not an extraneous solution.
Hence, this equation does not have any extraneous solution.
Answer: No, the friend is correct. In any function, each input value can only lead to one output value. When you input 3 for the x-values, you would get two output values because 3 is included in both equations. To fix this, you need to have the 3 not included in one of the equations.
For example, you could say or
because the input value of 3 would not be included twice.
If you look at the attached screenshot, you will see that if you keep your friend's function, inputting 3 will result in two outputs of 4 and -3, so therefore, cannot represent a piecewise function.
