Special Operatons in Algebra

Example corresponding to question 5 in algebra_1.

Example 1


The operation $\bigotimes$ is defined by $x \bigotimes y = -x^3+4y+2$. If $1 \bigotimes y = - 7$, then $y=$

  1. $-3$
  2. $3$
  3. $-2$
  4. $4$
  5. $-5$

Solution

This example is about solving quesions related special operators given their definition.

  1. Let us first use the definition of the operation $\bigotimes$ to write the following

    $1 \bigotimes y = -(1)^3+4y+2$

    Substitute $1 \bigotimes y$ by $-7$ in the equation above to obtain

    $-7 = -(1)^3+4y+2$

    Simplify the terms in the above equation and solve it

    $-7 = -1+4y+2$

    $-7 = 1+4y$

    $4y = -8$

    $y = - 2$
    Answer C