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Question
If f(x) = 2x – 1, g(x) = `(x + 1)/(2)`, show that fog = gof = x
Solution
f(x) = 2x – 1, g(x) = `(x + 1)/(2)`
fog = f[g(x)]
= `"f"[(x + 1)/2] - 1`
= `2 [(x + 1)/2] - 1`
= x + 1 – 1
= x
gof = g[f(x)]
= g(2x – 1)
= `(2x - 1 + 1)/2`
= `(2x)/2`
= x
∴ fog = gof = x
Hence it is proved.
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