Find the domain of 17ac 5 Solutiona The domain of the functi

Find the domain of:

Solution

a) The domain of the function g(x) = (17x -5)/ (3 - 2x) is { x R : 2x < 3 } Here 3 - 2x cannot be either 0 or negative. When 3 - 2x = 0, the division by 0 is not defined. Also, then 3 = 2x or, 2x = 3. When 3 - 2x is negative , (3 - 2x) is imaginary. Also, then   2x > 3.

b) The domain of the function h(x) = (2x + 5) /(x²+ x – 6) is { x R : -5/2   x < 2 or, x > 2} > we may observe that the numeratior (2x + 5) will not be real if (2x + 5) < 0 i.e. if x < -5/2 so that we must have  -5/2   x. Also, when x = 2, the denominator (x² + x – 6) = 0. Since division by 0 is not defined, we must have either x < 2 or, x > 2