Question

Help please?

Answer 1

B : `a=-1, b=3`.

Explanation:

A correction : `f(x)=-3x+18, if color(red)(b lt x)`.

Knowing that, `f` is continuous at `x=a`, we must have,

`lim_(x to a-)f(x)=f(a)=lim_(x to a+).............(ast)`.

`"Now, as "x to a-, x lt a. :. f(x)=1/4x+5/4..."[defn. of "f]`.

`:. lim_(x to a-)f(x)=lim_(x to a-)(1/4x+5/4)=1/4a+5/4...(ast^1)`.

Likewise, `lim_(x to a+)f(x)=lim_(x to a+)(2x+3)=2a+3...(ast^2)`

Since, `f(a)=1/4a+5/4`, we have, by `(ast), (ast^1) & (ast^2)`,

`1/4a+5/4=2a+3 rArr a=-1`.

Similarly, we can find `b=9`.

Hence, the right choice is B : `a=-1, b=3`.

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