90 ! need asap ! create a function y=f(x) that has a removable discontinuity at x=2 and a non-removable discontinuity at x=3. show work and step by step on how you got it.

step-by-step explanation:

the denominator in choice a factors to (x-2)(x+1). we have a pair of "x-2" terms that cancel leaving us with 1/(x+1). we cannot plug x = -1 into the simplified result because it leads the denominator x+1 to turn into 0.

also, we cannot plug x = 2 into p(x) for choice a either. it doesn't lead to issues for 1/(x+1) but the original function before we simplify will have x = 2 lead to a division by zero error.

a vertical asymptote is located at x = -1

the removable discontinuity happens when x = 2, so there will be a hole here.

got any answer chocies

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

let's solve your equation step-by-step.

24−3x=−27

step 1: simplify both sides of the equation.

24−3x=−27

24+−3x=−27

−3x+24=−27

step 2: subtract 24 from both sides.

−3x+24−24=−27−24

−3x=−51

step 3: divide both sides by -3.

−3x

−3

=

−51

−3

x=17

answer:

x=17

step-by-step explanation:

mark brainliest and have a great day!