Question

Need help finding two values of a continuous function that make it continuous at 5

Answer 1

We have

`\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)b-2x=b-10`

`\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)-(150)/(x-b)=(150)/(b-5)`

with
`f(5)` equal to the limit from the right as
`x\to5`.

We need to get

`b-10=(150)/(b-5)\implies(b-5)(b-10)=150\implies b^2-15b-100=(b-20)(b+5)=0`

`\implies b=20\text{ or }b=-5`

The larger solution in absolute value is
`b=20`.