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if-f-x-kx-3-2x-5-is-a-constant-function-then-what-will-be-the-value-of-k-




Question Number 180729 by sciencestudent last updated on 16/Nov/22
if f(x)=((kx+3)/(2x−5))   is a constant function  then what will be the value of k?
$${if}\:{f}\left({x}\right)=\frac{{kx}+\mathrm{3}}{\mathrm{2}{x}−\mathrm{5}}\:\:\:{is}\:{a}\:{constant}\:{function} \\ $$$${then}\:{what}\:{will}\:{be}\:{the}\:{value}\:{of}\:{k}? \\ $$
Answered by srikanth2684 last updated on 16/Nov/22
f′(x)=0  ((k(−5)−(3)(2))/((2x−5)^2 ))=0  −6=5k  ((−6)/5)=k
$${f}'\left({x}\right)=\mathrm{0} \\ $$$$\frac{{k}\left(−\mathrm{5}\right)−\left(\mathrm{3}\right)\left(\mathrm{2}\right)}{\left(\mathrm{2}{x}−\mathrm{5}\right)^{\mathrm{2}} }=\mathrm{0} \\ $$$$−\mathrm{6}=\mathrm{5}{k} \\ $$$$\frac{−\mathrm{6}}{\mathrm{5}}={k} \\ $$
Answered by mr W last updated on 16/Nov/22
((kx+3)/(2x−5))=c  (k−2c)x+3+5c=0  3+5c=0 ⇒c=−(3/5)  k−2c=0 ⇒k=−(6/5)
$$\frac{{kx}+\mathrm{3}}{\mathrm{2}{x}−\mathrm{5}}={c} \\ $$$$\left({k}−\mathrm{2}{c}\right){x}+\mathrm{3}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{3}+\mathrm{5}{c}=\mathrm{0}\:\Rightarrow{c}=−\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${k}−\mathrm{2}{c}=\mathrm{0}\:\Rightarrow{k}=−\frac{\mathrm{6}}{\mathrm{5}} \\ $$

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