Question

Find the value(s) of 'a' so that f(x) is continuous at x = 2, where; f(x) = ax-3 and x/a
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Answer 1

Answer:

${\bf{\red{ANSWER \: \: }}}$

A=1,2

Step-by-step explanation:

Given, f(x)={ax+3,a2x−1x≤2x>2

Continuity at x=2,

LHL=x→2−limf(x)=x→2lim(ax+3)=2a+3

RHL=x→2+limf(x)=x→2lim(a2x−1)=2a2−1

Since, f(x) is continuous for all values of x.

Therefore, LHL= RHL

⇒2a+3=2a2−1

⇒2a2−2a−4=0

⇒a2−a−2=0

⇒a2−2a+a−2=0

⇒a(a−2)+1(a−2)=0

⇒(a+1)(a−2)=0

⇒a=−1,2

Answer 2

Answer:

ANSWER

A=1,2

Step-by-step explanation:

Given, f(x)={ax+3,a2x−1x≤2x>2

Continuity at x=2,

LHL=x→2−limf(x)=x→2lim(ax+3)=2a+3

RHL=x→2+limf(x)=x→2lim(a2x−1)=2a2−1

Since, f(x) is continuous for all values of x.

Therefore, LHL= RHL

⇒2a+3=2a2−1

⇒2a2−2a−4=0

⇒a2−a−2=0

⇒a2−2a+a−2=0

⇒a(a−2)+1(a−2)=0

⇒(a+1)(a−2)=0

⇒a=−1,2