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If the function f(x)= array ll a+b x, & x 1 5, & x=1 b-a x, & x 1 array . is continuous, then what is the value of (a+b) ?

Options

  1. A5
  2. B10
  3. C15
  4. D20

Correct answer

A. 5

Step-by-step solution

f(x)= array lc a+b x, & x 1 5, & x=1, is continuous b-a x, & x 1 array . aligned & _ x 1⁻ f(x)= _ x 1⁺ f(x)=f(1) & _ x 1⁻ (a+b x)= _ x 1⁺ (b-a x)=5 aligned a+b=5 (i) and b-a=5 . (ii) From (i) and (ii) b=5 and a=0 a+ b =0+5=5

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