Answer:
[tex]x=\sqrt[3]{10}-2[/tex]
Step-by-step explanation:
The composite function (f(x+1)) is moved in the x-axis by -1, you know this by solving x+1=0.
The equivalent expresion for f(x+1) is
[tex]f(x+1)= (x-1+3)^{3}+4[/tex]
[tex]f(x+1)=(x+2)^{3}+ 4[/tex]
Eval the above expression in g(x)
[tex]g(x)=(x+2)^{3}+4-2[/tex]
We must find x that gives g(x)=12
The equation is the following
[tex]12=(x+2)^{3}+2[/tex]
Grouping terms>
[tex](x+2)^{3} =10[/tex]
To solve for x, must apply cubic root in both sides of equation:
[tex]\sqrt[3]{(x+2)^{3} } =\sqrt[3]{10}[/tex]
it then turns in the following>
[tex]x+2=\sqrt[3]{10}\\[/tex]
Giving the stated answer
