Answer:
g(x)= x+1
Step-by-step explanation:
[tex]h(x)= (fog)(x)= f(g(x))[/tex]
Given [tex]f(x)= \sqrt[3]{x+2}[/tex], [tex]f(x)= \sqrt[3]{x+3}[/tex]
[tex]f(g(x))= \sqrt[3]{x+3}[/tex]
[tex]f(x)= \sqrt[3]{x+2}[/tex]
Replace x with g(x)
[tex]f(g(x))= \sqrt[3]{g(x)+2}[/tex]
Now we need to find out what we plug in for g(X) to get x+3 under the radical
g(x) +2 is under the radical. we need x+3 , so we replace g(x) with x+`
So g(x)+2 becomes x+1+2 is x+3
Hence g(x) is x+1
