# If fog(x) = x – 3 and f(x) = x^2, what is g(x).

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### 2 Answers

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)**

fog(x) = f(g(x))

If f(g(x)) =x - 3 and f(x) = x^2

f(g(x)) = (g(x))^2

But f(g(x)) = x - 3 => (g(x))^2 =x - 3

To determine g(x), we'll apply square root both sides:

sqrt(g(x))^2 = sqrt(x-3)

**g(x) = sqrt(x-3)**