Question

Find (f o g)(1) for the following functions. Round your answer to two decimal places, if necessary.

Answer 1

By definition:

$(f\circ g)(x)$

It is a Function Compositon. It means that you must substitute the function g(x) into the function f(x).

For this case:

$\begin{gathered} f(x)=2+\sqrt[]{x} \\ g(x)=\sqrt[]{x+24} \end{gathered}$

Substitute the function g(x) into the function f(x):

$(f\circ g)(x)=2+\sqrt[]{\sqrt[]{x+24}}$

Simplify:

$(f\circ g)(x)=2+\sqrt[4]{x+24}$

Now, substitute this value into the Composite function and evaluate:

$x=1$

You get:

$\begin{gathered} (f\circ g)(1)=2+\sqrt[4]{1+24} \\ (f\circ g)(1)=2+\sqrt[4]{25} \\ (f\circ g)(1)=2+\sqrt[4]{5^2} \\ (f\circ g)(1)=2+\sqrt[]{5} \end{gathered}$