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Question
Match the following function
Domain Range
1. coshx a) R
2. cosh−1x b) (0,∞)
3. sech−1 c) [1,∞)
4. coth−1 d) R−[−1,1]
Match the following function
Domain Range
1. coshx a) R
2. cosh−1x b) (0,∞)
3. sech−1 c) [1,∞)
4. coth−1 d) R−[−1,1]
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Solution
The correct option is A c,a,b,d
cosh(x)=ex+e−x2
Hence domain is R and range is [1,∞)
arcoth(x)=12ln(x+1x−1) ...(for|x|>1)
Hence range is R−0.
arcsech(x)=ln(1+√1−x2x) for 0 Hence range is[0,∞).
Domain Range
coshx [1,∞]cosh−1 Rsech−1 (0,∞)coth−1 R−[−1,1]Hence, the answers are c,a,b,d.
cosh(x)=ex+e−x2
Hence domain is R and range is [1,∞)
arcoth(x)=12ln(x+1x−1) ...(for|x|>1)
Hence range is R−0.
arcsech(x)=ln(1+√1−x2x) for 0 Hence range is[0,∞).
Hence domain is R and range is [1,∞)
arcoth(x)=12ln(x+1x−1) ...(for|x|>1)
Hence range is R−0.
arcsech(x)=ln(1+√1−x2x) for 0 Hence range is[0,∞).
Domain Range
coshx [1,∞]
cosh−1 R
sech−1 (0,∞)
coth−1 R−[−1,1]
Hence, the answers are c,a,b,d.
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