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Question
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
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Solution 1
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
If x < 0, x + 7 < 7
If x ≥ 0, – x ≤ 0 so that 8 – x ≤ 8
∴ Range = `(- ∞, 8)`
∴ for y = 10, we cannot find x such that f(x) = y
∴ f is not onto
∴ f–1 does not exist.
Solution 2
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
∴ f(– 1) = – 1 + 7 = 6
∴ f(2) = 8 – 2 = 6
∴ f(– 1) = f(2) but – 1 ≠ 2
∴ f is not one-one
∴ f–1 does not exist.
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