Question

If f: R → R defined by f(x) = x4 + 2 then the value of f-1(83) and f-1(-2) respectively are.

(a) ϕ, {3, -3}

(b) {3, -3}, ϕ

(c) {4, -4}, ϕ

(d) {4, -4}, {2, -2}

Answer 1

The correct option (b) {3, -3}, ϕ

Explanation:

f(x) = x4 + 2 = y ⇒ x = (y - 2)1/4

⇒ f–1(x) = (x - 2)1/4

⇒ f–1(83) = (81)1/4 = ± 3 and f–1(–2) = (4)1/4 = ϕ