Q1 of 215 Page 2

Find gof and fog when f: R → R and g: R → R is defined by

f(x) = 8x3 and g(x) = x1/3

Since, f:R → R and g:R → R


fog:R → R and gof:R → R


f(x) = 8x3 and


Now, gof(x) = g(f(x)) = g(8x3)



gof(x) = 2x




fog(x) = 8x


Thus, gof(x) = 2x and fog(x) = 8x


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1

Find gof and fog when f: R → R and g: R → R is defined by

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 1

Find gof and fog when f: R → R and g: R → R is defined by

f(x) = x2 + 2x – 3 and g(x) = 3x – 4

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Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5, 9)}. Show that gof and fog are both defined, Also, find fog and gof.

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Let f = {(1, – 1), (4, – 2), (9, – 3), (16, 4)} and g = {(– 1, – 2), (– 2, – 4), (– 3, – 6), (4, 8)}. Show that gof is defined while fog is not defined. Also, find gof.