1)y={(sqrt(-x), -4 <= x <= 0),(sqrt x, 0 < x <= 4):}2)y={(-x-2, -2 <= x <=-1),(x, -1<x<=1),(-x+2, 1 < x <=2):}Piecewise-Defined Functions. Find the (a) domain and (b) range.

defazajx

defazajx

Answered question

2020-10-21

1)y={x4x0x0<x4
2)y={x22x1x1<x1x+21<x2
Piecewise-Defined Functions. Find the (a) domain and (b) range.

Answer & Explanation

unett

unett

Skilled2020-10-22Added 119 answers

Step 1
1)y={x4x0x0<x4
For x0x is real, for x0,x is real.
y is real for X[4,4].
Hence the domain of the functions is [4,4]
When x(0,4],x(0,2]
When x[4,0],x[0,4], hence x[0,2]
The set of all values y takes is [0,2]
Hence the range is [0,2]
Step 2
2)y={x22x1x1<x1x+21<x2
The given functions is defined for x[2,2]
Hence the domain of the function is [2,2]
Range
i) When 2x1
Multiplying by -1 throughput the inequality,
2x1
1x2
Subtracting by 2 through out
1x20
So, y=(x2)[1,0]
ii) When x[1,1],y=x, hence y[1,1]
iii) When 1<x2
1x2
2x<1
Adding 2 throughout
0x+2<1
Hence when 1<x2,y[0,1)
So, the set of all values that y takes is [1,1]
Hence the range is [1,1]

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