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Question
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = `(2)/x`, g(x) = 2x2 – 1
Solution
f(x) = `(2)/x`, g(x) = 2x2 – 1
fog = f[g(x)]
= f(2x2 – 1)
= `(2)/(2x^2 - 1)`
gof = g[f(x)]
= `g(2/x)`
= `2(2/x)^2 - 1`
= `2 xx 4/x^2 - 1`
= `8/x^2 - 1`
fog ≠ gof
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