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If-f-x-x-2-4x-3-g-x-7-x-0-x-lt-7-5x-5x-x-7-R-fog-a-b-find-the-value-of-b-a-R

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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) }
If,f(x)=−x2+4x−3,g(x)={7−x0⩽x<7⌊5x⌋−5xx⩾7⇒Rfog=(a,b]findthevalueofb−aRfog={(fog)(x)∣x∈Dfog}
Answered by mehdee7396 last updated on 04/Oct/24
R_g =(−1,0]∪(0,(√7)]=(−1,(√7)] f(x)=−(x−2)^2 +1 x∈D_g ⇒−1<x≤(√7)⇒−3<x−2≤−2+(√7) 0≤(x−2)^2 <9 −9<−(x−2)^2 ≤0 −8<R_(fog) ≤1 ⇒b−a=9 ✓
Rg=(−1,0]∪(0,7]=(−1,7]f(x)=−(x−2)2+1x∈Dg⇒−1<x⩽7⇒−3<x−2⩽−2+70⩽(x−2)2<9−9<−(x−2)2⩽0−8<Rfog⩽1⇒b−a=9✓
Commented by mnjuly1970 last updated on 04/Oct/24
thabks alot sir mehdee
thabksalotsirmehdee

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