Answer:
The correct answer is:
[tex]g(x) = x+1[/tex]
Step-by-step explanation:
Given that:
[tex]h(x) = f\circ g(x)= \sqrt[3]{x+3}[/tex]
[tex]f(x) = \sqrt[3]{x+2}[/tex]
To find:
[tex]g(x) = ?[/tex]
Solution:
Let [tex]g(x) = m[/tex]
We have
[tex]f\circ g(x)= \sqrt[3]{x+3}\\OR\\f( g(x))= \sqrt[3]{x+3}[/tex]...... (1)
Now, we have let:
[tex]g(x) = m\\\therefore f(g(x)) = f(m)[/tex]
Putting x = in f(x), we get
[tex]f(x) = \sqrt[3]{x+2}\\\Rightarrow f(m) = \sqrt[3]{m+2}[/tex]....... (2)
Comparing equation (1) and (2):
[tex]\sqrt[3]{x+3} =\sqrt[3]{m+2}[/tex]
Taking cubes both sides:
[tex]x+3=m+2\\\Rightarrow m = x+3-2\\\Rightarrow m = x+1[/tex]
[tex]\therefore g(x) = x+1[/tex]
Hence,
The correct answer is:
[tex]g(x) = x+1[/tex]
