Answer:
True
Step-by-step explanation:
given [tex]f(x)=\sqrt[4]{2x-6}[/tex] and [tex]g(x)=\frac{1}{2} x^{4}+3[/tex]
to find the inverse we just switch the x and y values for one of the functions,
in this case I will chose f(x) [note f(x) is just another way of saying y]
[tex]x=\sqrt[4]{2y-6}[/tex]
solve for x;
raise both sides to the 4th power
[tex]x^{4}=2y-6[/tex]
add 6 to both sides
[tex]x^{4} +6=2y-6-6\\=x^{4}+6=2y[/tex]
divide both sides by 2 and you get
[tex]\frac{x^{4} +6}{2} =\frac{2}{2} y[/tex]
simplify and you get
[tex]y=\frac{1}{2} x^{4} +3[/tex]
which equals to g(x).
hope this helps, for practice, I would recommend you switch the x and y of g(x)
