Question

Given that f(x)=8x+4 and g(x)=1-x^2, calculatea) f(g(0))b) g(f(0))

Answer 1

The notation f(g(x)) means that you have to calculate the composition of the functions, that is, calculate f(x) when x=g(x)

Item a f(g(0))

You have to calculate f(x) when x=g(0)

The first step is to calculate g(0) → i.e. g(x) for x=0

You have to replace the function with x=0 and calculate its value:

`\begin{gathered} g(x)=1-x^2 \\ g(0)=1-0^2 \\ g(0)=1 \end{gathered}`

Now that we have determine the value of g(0), you have to replace it in f(x)

`\begin{gathered} f(x)=8x+4 \\ f(g(0))=8\cdot(g(0))+4 \\ f(g(0))=8\cdot1+4 \\ f(g(0))=12 \end{gathered}`

Item b g(f(0))

In this item you have to calculate g(x) when x=f(0)

The first step is to calculate f(x) for x=0

`\begin{gathered} f(x)=8x+4 \\ f(0)=8\cdot0+4 \\ f(0)=4 \end{gathered}`

Once you calculated the value of f(0), you have to replace its value in the function g(x)

`\begin{gathered} g(x)=1-x^2 \\ g(f(0))=1-(f(0))^2 \\ g(f(0))=1-4^2 \\ g(f(0))=1-16 \\ g(f(0))=-15 \end{gathered}`

So the results are

`\begin{gathered} a)f(g(0))=12 \\ b)g(f(0))=-15 \end{gathered}`