Question

Find the domain and range of the following function.

f(x) = `sqrt(16 - x^2)`

Answer 1

f(x) = `sqrt(16 - x^2)`

For f to be defined,

16 – x² ≥ 0

∴ x² ≤ 16

∴ – 4 ≤ x < 4

∴ Domain of f = [– 4, 4]

Clearly, f(x) ≥ 0 and the value of f(x) would be maximum when the quantity subtracted from 16 is minimum i.e. x = 0

∴ Maximum value of f(x) = `sqrt(16)` = 4

∴ The range of f = [0, 4]