Please give an example of another function whose inverse is only defined if we restrict the domain of the original function.
2 answers:
Answer:
f(x) = x^2
Step-by-step explanation:
The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.
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The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.
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Given :
Nathan smiled at 50 people one day and recorded that 36 people smiled back at him.
To Find :
How many people should Nathan expect to return a smile if he smiles at 650 people over a period of time.
Solution :
Ratio of people smiled by total number of people is :
Now, it is given that we have to use the given conditions.
Therefore, ratio will be same :
Therefore, number of smiles Nathan expect to return is 468.