g(x) =(2x^2-3x-20)/(x-4), if x!=4 and =kx-15, if x=4. Evaluate the constant k that makes the function continuous.

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-09-12

g(x)
=2x23x20x4,ifx4
and
=kx15, if x=4
Evaluate the constant k that makes the function continuous.

Answer & Explanation

Layton

Layton

Skilled2021-09-13Added 89 answers

For f(x) to be continuous at a point x=a:
limxa+f(x)=limxaf(x)=f(a)
It's given that g(x) is continuous at x=4, so
limx4+g(x)=limx4g(x)=g(4)
limx4g(x)=g(4)
limx42x23x20x4=k(4)15
limx42x28x+5x20x4=4k15
limx42x(x4)+5(x4)x4=4k15
limx4(2x+5)(x4)x4=4k15
limx4(2x+5)=4k15
2(4)+5=4k-15
k=7

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