Question

Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your answer.
f(x) = negative 8 x + 4. y = negative 8 x + 4. y minus 4 = negative 8 x. x = (y minus 4) divided by negative 8. f Subscript negative 1 Baseline (x) = (y minus 4) divided by negative 8.

Answer 1

Talib’s algebra (solving y = −8x + 4 for x) is correct up to the last step: from y − 4 = −8x he gets x = (y − 4)/(−8). But when writing the inverse as a function he should replace y by x. So the inverse is

f⁻¹(x) = (x − 4)/(−8) = (4 − x)/8.

You can check: f(f⁻¹(x)) = −8·((4 − x)/8) + 4 = −(4 − x) + 4 = x, so this is correct.

(Equivalent forms: f⁻¹(x) = (4 − x)/8 = −(1/8)x + 1/2.)