Question

The binary operation $\ast :R\times R\to R$ is defined as $a\ast b=2a+b$. Find $(2\ast 3)\ast 4.$

Answer 1

Since $a\ast b=2a+b$

Put $a=2$ and $b=3$ in $a\ast b=2a+b$ as shown below:

$2\ast 3=2\left(2\right)+3=4+3=7$

We have to find $(2\ast 3)\ast 4$ that is to find $7\ast 4$.

Now put $a=7$ and $b=4$ in $a\ast b=2a+b$ as shown below:

$7\ast 4=2\left(7\right)+4=14+4=18$.

Hence $(2\ast 3)\ast 4=18.$