Theory question 101
FunctionsTwo functions g and h are defined on the set R of real numbers by g : x → x2 − 2 and h : x → 1/(x + 2), x ≠ −2. Find: (a) h−1, the inverse of h; (b) g∘h when x = −½
Show the model answer
Model answer
(a) Let y = 1/(x + 2); then x + 2 = 1/y, x = 1/y − 2
h−1(x) = 1/x − 2 = (1 − 2x)/x, x ≠ 0
(b) h(−½) = 1/(3/2) = 2/3
g(2/3) = 4/9 − 2 = −14/9
Explanation
For g∘h apply h first, then g.