11
QuizMultiple Choice

Comparing a Function and Its Inverse — Quiz

Question 11 • Precalculus

Which is an accurate comparison of the functions?

Answer
A
The reciprocal of the slope of f of x is the same as the slope of f inverse of x .
B
The opposite of the y - coordinate of the y -intercept of f of x is the same as the x -coordinate of the x -intercept of f inverse of x .
C
The negative reciprocal of the slope of f of x is the same as the slope of f inverse of x .
D
The y - coordinate of the y -intercept of f of x is the same as the y -coordinate of the y -intercept of f inverse of x .

Explanation

For a linear function with slope m, its inverse swaps the input and output, so the inverse has slope 1/m (assuming m is nonzero). That is the reciprocal of the original slope, making A, “The reciprocal of the slope of f of x is the same as the slope of f inverse of x,” accurate. The inverse’s slope is not generally the negative reciprocal.

AI-written and checked against the verified answer.

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