Given f(x) = 2* and g(x) = 2x + 1 evaluate (f?g)(o) and (g?f)(2).

Question

asked Aug 5, 2023 29.9k views

1 Answer

Verdi · Answer 1 · 2023-08-09T06:44:35+0000

The given functions are

$\begin{gathered} f(x)=2^z \\ g(x)=2x+1 \end{gathered}$

First, we have to find the composite function

$(f\circ g)(x)$

We have to enter g(x) inside f(x), as follows

$(f\circ g)(x)=2^((2x+1))$

Now, we evaluate this composition when x = 0.

$(f\circ g)(0)=2^((2(0)+1))=2^1=2$

Now, we find the second composition, this time we have to enter f(x) inside g(x).

$(g\circ f)(x)=2(2^x)+1$

We evaluate the composition when x = 2.

$(g\circ f)(2)=2(2^2)+1=2(4)+1=8+1=9$