What is the largest possible domain for the function fx x

What is the largest possible domain for the function f(x) = x + (4 – x²) ?

a. {x: 0 x 2, x R}

b. {x: -2 x 2, x R}

c. {x: 0 x 4, x R}

d. {x: x ³ 2, x R}

Solution

for x -domain will be all +ve value of x .Hence, x>=0

for (4 – x2) -for domain 4-x^2 >=0 -> x^2<=4 , -2<=x<=2

hence ,final domain calculated by compairing both domains

hence answer is a) {x: 0 x 2, x R}