Question

How do you solve question 1

Answer 1

9514 1404 393

Answer:

(A) 1 only

Explanation:

Factor numerator and denominator and see what cancels.

`f(x)=(2x^2+14x-16)/(x^2-9x+8)=(2(x-1)(x+8))/((x-1)(x-8))=(x-1)/(x-1)\cdot(2(x+8))/(x-8)\\\\f(x)=(2x+16)/(x-8)\qquad x\\e1`

The factor of x-1 in the original denominator means the expression is undefined at x=1. The reduced expression is defined there, so the discontinuity at x=1 could be removed by defining f(1) = -18/7.

There is a removable discontinuity at x=1 only. The discontinuity at x=8 is a vertical asymptote where the function changes sign. It cannot be removed by defining a value for the function there.