We have fog(x) = f(g(x)) = x – 3 and f(x) = x^2 and we need to determine g(x).

Let g(x) = y

=> f(y) = y - 3 = x^2

=> x = sqrt (y – 3)

interchanging x with y gives y = g(x) = sqrt (x –...

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We have fog(x) = f(g(x)) = x – 3 and f(x) = x^2 and we need to determine g(x).

Let g(x) = y

=> f(y) = y - 3 = x^2

=> x = sqrt (y – 3)

interchanging x with y gives y = g(x) = sqrt (x – 3)

Check: f(g(x)) = f( sqrt (x – 3)) = [sqrt (x – 3)]^2 = x – 3.

**Therefore g(x) = sqrt (x – 3)**