consider the function f(x)=3x^2-12/x^2+2x. If f(x)=3, what is x?

Answer 1

No 3 is not in the range of this function.

You can either factor it or cross multiply.

Factoring : (3x^2 – 12) / (x^2+2x) =

                 3(x+2)(x-2)/(x(x+2)) =

             3(x-2)/x =

  3 ( 1 – 2/x)

For this to be 3, it is 1 – 2/x = 1

                                -2/x = 0

                        -2 = 0 shows there is not solution.

Cross multiplication gives: 3(x^2-4) = 3x(x+2)

                                3x^2 – 12 = 3x^2 + 6x

                    -12 = 6x

                X = -2

However, -2 is not in the domain of the function as it causes division by zero.

There 3 is not in range

Answer 2

f(x)=(3x²-12)/(x²+2x) Domain All real numbers except where denominator is zero x≠-2, x≠0

f(x)=3

3=(3x²-12)/(x²+2x)

Multiply each side by the denominator

3(x²+2x)=3x²-12

3x²+6x=3x²-12

subtract 3x² from both sides

3x²+6x=3x²-12

6x=-12

x=-2 Cant work because not in domain.

No solution