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joja [24]
3 years ago
8

Given the function f(x) = 3 (x - 9) + 6 which of the following represents f-1 (x)?

Mathematics
1 answer:
igomit [66]3 years ago
5 0

Answer:

f^{-1}(x) = \frac{1}{3} x + 7

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 3(x - 9) + 6 ← distribute and simplify right side

y = 3x - 27 + 6 = 3x - 21 ( add 21 to both sides )

y + 21 = 3x ( divide all terms by 3 )

\frac{1}{3} y + 7 = x

Change y back into terms of x with x = f^{-1}(x) , thus

f^{-1}(x) = \frac{1}{3} x + 7

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