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Question
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = `(x + 6)/3`, g(x) = 3 – x
Solution
f(x) = `(x + 6)/3`, g(x) = 3 – x
fog = f[g(x)]
= f(3 – x)
= `(3 - x + 6)/3`
= `(9 - x)/3`
gof = g[f(x)]
= `"g"((x + 6)/3)`
= `3 - ((x + 6))/3`
= `(9 - x - 6)/3`
= `(3 - x)/3`
fog ≠ gof
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