Question

f(x) = x² + 2 find the range​

Answer 1

Answer:

1

mohinderRattan

19.08.2015

Math

Secondary School

+5 pts

Answered

Find the range and domain of followingfunctions

f(x) = whole root(2 + x - x2)

1

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gohan 

 

Expert

F(x)=√2+x-x²

let f(X) = y

y=√2+x-x²

squaring both sides 

y²=2+x-x²

y² is always a positive number so it means that f(X)≥0

2+x-x²≥0

multiply the whole equation by (-)1

x²-x-2≤0 because inquality sign changes

factorise it

x²-2x+x-2≤0

x(x-2)+1(x-2)≤0

(x+1)(x-2)≤0

x=-1and +2 

so there are three cases 

 - infinity    +   -1         -          2         +      +infinity

↑-----------------↑----------------↑-----------------↑

mean domain of this function is [-1,2]   

--------------------------------------------------

for range of the function 

x²-x-2≤0

by completing square method

(x²-x/2 - 1/4 -2 ≤ 0

(x-1/2)² +  -1/4 -2 ≤0

(x-1/2)²≤9/4

x-1/2≤+-3/2

x≤+3/2+1/2=2

and x≤-3/2+1/2=-1

so minimum value of this function is -1 and maximum value of this function is 2 so range of the fuction ∈[-1 ,2] 

Answer 2

So range of the function is [2, infinity). You can also have another approach. This can be applied to most of the problems. Let y=x