find the domain f(x) =√x-3 + √x-4/x
Answers
Answered by
0
Given,
f(x)=
(x−3)−2
x−4
−
x−3+2
x−4
for f(x) to be defined we need to have
x−3−2
x−4
≥0−(1)
x−3+2
x−4
≥0−(2)
x−4≥0−(3)
Solving (1)
x−3≥2
x−4
⇒x
2
+9−6x≥4(x−4)
⇒x
2
+9−6x≥4x−16
⇒x
2
−10x+25≥0
⇒(x−5)
2
≥0
Solving (2)
x−3≥−2
x−4
⇒x
2
+9−6x≥4
x−4
⇒(x−5)
2
≥0
Solving (3)
x−4≥0
⇒x≥4
So the solution will be the intersection of the three regions found above which is
xϵ[4,∞)
Answered by
1
Given,
f(x)=
(x−3)−2
x−4
−
x−3+2
x−4
for f(x) to be defined we need to have
x−3−2
x−4
≥0−(1)
x−3+2
x−4
≥0−(2)
x−4≥0−(3)
Solving (1)
x−3≥2
x−4
⇒x
2
+9−6x≥4(x−4)
⇒x
2
+9−6x≥4x−16
⇒x
2
−10x+25≥0
⇒(x−5)
2
≥0
Solving (2)
x−3≥−2
x−4
⇒x
2
+9−6x≥4
x−4
⇒(x−5)
2
≥0
Solving (3)
x−4≥0
⇒x≥4
So the solution will be the intersection of the three regions found above which is
xϵ[4,∞)
Similar questions