Question

Which values of a and b are continuous at every x?

Answer 1

To find:

The value of a and b.

Solution:

The given function g(x) is continuous at every x.

At x = 0, we have:

`\begin{gathered} 2ax-3b=x^2-2a-7b \\ -3b=-2a-7b \\ 2a=-4b \\ a=-2b \end{gathered}`

At x = 1, we have:

`\begin{gathered} x^2-2a-7b=5x-3 \\ 1-2a-7b=5-3 \\ -2a-7b=1 \\ 2a+7b=-1 \end{gathered}`

Substitute a = -2b:

`\begin{gathered} 2(-2b)+7b=-1 \\ -4b+7b=-1 \\ 3b=-1 \\ b=-(1)/(3) \end{gathered}`

Now, a = -2b. So,

`\begin{gathered} a=-2(-(1)/(3)) \\ a=(2)/(3) \end{gathered}`