Question

Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-fifth x minus four-fifths?
f Superscript negative 1 Baseline (x) = negative one-fifth x + four-fifths
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Answer 1

Let y = f⁻¹(x) = −(1/5)x − 4/5. Solve for x:

y = −(1/5)x − 4/5
y + 4/5 = −(1/5)x
x = −5(y + 4/5) = −5y − 4

Swap x and y to get f(x) = −5x − 4.

(Check: f(f⁻¹(x)) = −5(−1/5 x − 4/5) − 4 = x.)