Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your
2 answers:
Given the function
The inverse of the function is calculated by changing f(x) to y and making x the subject of the formula as follows:
We now change back the variables to get the function in the form of inverse function as follows:
Comparing this with Talib's work, we can see that he is correct except for the last line where he did not change the variable y back to x.
Therefore, the last line of his work made his inverse not to be correct.
The inverse of the function is calculated by changing f(x) to y and making x the subject of the formula as follows:
We now change back the variables to get the function in the form of inverse function as follows:
Comparing this with Talib's work, we can see that he is correct except for the last line where he did not change the variable y back to x.
Therefore, the last line of his work made his inverse not to be correct.
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Just did a specific one of these; let's do the general case.
The point nearest the origin is (a,b).
The line from the origin through the point is
The line we seek is perpendicular to this one. We swap the coefficients on x and y, negating one, to get the perpendicular family of lines. We set the constant by plugging in the point (a,b):
That's standard form; let's plug in the numbers: