Question

Let f (x) = x– 3 and g(x) = x² – 7. Find g (f(x))

Answer 1

We are given the following functions:

`\begin{gathered} f(x)=x-3 \\ g(x)=x^2-7 \end{gathered}`

We are asked to find:

`g(f(x))`

That means that in the function g(x), wherever we find "x" we are going to replace it with the value of the function f(x}, like this:

`g(f(x))=(x-3)^2-7`

Now we simplify the parenthesis using the following property:

`(a\pm b)^2=a^2\pm2ab+b^2`

Applying the property we get:

`g(f(x))=x^2-6x+9-7`

Now we solve the operations:

`g(f(x))=x^2-6x+2`