Question

The exact number of kilometers in m miles is f(m), where f is the function defined by f(m) = 1.609344m. (a) find a formula for f−1(k). (b) what is the meaning of f−1(k)?

Answer 1

• f⁻¹(k) = k/1.609344
• f⁻¹(k) is the exact number of miles in k kilometers

Explanation:

(a) If we let k = f(m), we can solve for m to find f⁻¹(k).

k = 1.609344m

k/1.609344 = m = f⁻¹(k)

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(b) Since k is the number of kilometers in m miles, m is the number of miles in k kilometers.

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In summary ...

(a) f⁻¹(k) = k/1.609344

(b) f⁻¹(k) is the exact number of miles in k kilometers