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Given f(x)=x²-3x - 23 and
g(x)=x-1, find (fog)(x).

Sagot :

The required function is (fog)(x) = x^2 – 5x – 19  

We have been given two functions which are:

 f(x) = x^2 – 3x – 23

 g(x) = x – 1

We need to find (fog)(x) which is also equal to f(g(x)).

In this, we have to replace x with the function g(x) in the function, f(x). numerically

    f(g(x)) = g(x)^2 – 3g(x) – 23    

Now we will write the value of g(x) in the above equation. We will get

         f(g(x)) = (x-1)^2 – 3(x-1) – 23

         f(g(x)) = x^2 + 1 – 2x – 3x + 3 – 23

         f(g(x)) = x^2 – 5x – 19

Hence  (fog)(x) = x^2 – 5x – 19  is the required function.

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