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There are exactly two distinct linear fu...

There are exactly two distinct linear functions, ______ and ______, which map [-1,1] onto [0,4].

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The correct Answer is:
`y=x+1 and y = -x+1`
Let `y = ax + b and y = cx + d` be two linear functions.
When `x = -1, y = 0 and x = 1, y = 2`, then
` 0 = -a + b and a+ b = 2 rArr a = b = 1`
`therefore y=x+1 " ...(i)" `
Again, when ` x = -1,y= 2 and x=1, y=0,` then
`-c+d=2 and c+d =0`
`rArr d=1 and c= -1`
` therefore y = -x+1 " ...(ii)" `
Hence, two linear functions are `y=x+1 and y=-x+1`
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