This is the graph of function $$f(x)=3[ ^3\sqrt{x}+4]$$ ![](http://admin.getprephub.com/media/editor/te20_20230117204610239452.png) What is the graph of $${g}({x})=3 ^3\sqrt{\frac{x}{2}}+4$$ ?

Here, $$f(x)=3 \quad ^3\sqrt{x}+4 $$ $$g(x) = f(k \cdot x) \cdot|k|<1, g(x)=3 ^3\sqrt{\frac{x}{2}}+4 $$ $$\text { so },k=\frac{1}{2} $$ $$|\frac{1}{2}| < 1$$ So, $$g$$ is a horizontal stretch of $$f$$. $$g(4)=3 ^3\sqrt{\frac{4}{2}}+4=3 ^3\sqrt{2}+4$$ Now,$$g(x)=10$$ gives $$3 [^3\sqrt{\frac{x}{2}}]+4=10$$ or, $$3 [^3\sqrt{\frac{x}{2} } ] =6$$ or, $$\quad ^3 \sqrt{\frac{x}{2}}=2$$ or, $$\quad \frac{x}{2}=2^3=8$$ or, $$x=16$$ $$\therefore g$$ passes through $$(16,10),(0,4)$$ The correct diagram is ![](http://admin.getprephub.com/media/editor/te20s1_20230117204849584114.png)