Question Number 212140 by mnjuly1970 last updated on 03/Oct/24
![If, f(x)=− x^2 +4x −3 , g(x)= { (( (√(7−x)) 0≤x <7)),(( ⌊ 5x ⌋ −5x x≥7)) :} ⇒ R_(fog) = (a ,b] find the value of b−a R_(fog) = { (fog)(x)∣ x∈ D_(fog) }](https://www.tinkutara.com/question/Q212140.png)
$$ \\ $$$$\:\mathrm{I}{f},\:\:\:\:\:{f}\left({x}\right)=−\:{x}^{\mathrm{2}} \:+\mathrm{4}{x}\:−\mathrm{3}\: \\ $$$$\:\:\:\:\: \\ $$$$,\:{g}\left({x}\right)=\:\begin{cases}{\:\sqrt{\mathrm{7}−{x}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\:<\mathrm{7}}\\{\:\:\lfloor\:\mathrm{5}{x}\:\rfloor\:−\mathrm{5}{x}\:\:\:\:\:\:\:\:{x}\geqslant\mathrm{7}}\end{cases}\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:{R}_{{fog}} \:=\:\left({a}\:,{b}\right]\:\: \\ $$$$\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:\:{b}−{a} \\ $$$$\:\:\:\:\:\:{R}_{{fog}} \:=\:\left\{\:\left({fog}\right)\left({x}\right)\mid\:{x}\in\:{D}_{{fog}} \:\right\} \\ $$