Theory question 103
FunctionsThe inverse of a function f is given by f−1(x) = (5x − 6)/(4 − x), x ≠ 4. Find the: (a) function, f(x) (b) value of x for which f(x) = 5.
Show the model answer
Model answer
(a) f is the inverse of f⁻¹. Let y = (5x − 6)/(4 − x): 4y − xy = 5x − 6, x(5 + y) = 4y + 6.
f(x) = (4x + 6)/(x + 5), x ≠ −5.
(b) (4x + 6)/(x + 5) = 5 gives 4x + 6 = 5x + 25, x = −19 (check: f⁻¹(5) = 19/(−1) = −19).
Explanation
The inverse of f⁻¹ is f itself.