We need to find the function [tex]f(g(x))[/tex]
The required function is [tex]f(g(x))=75x^4-35x^2+6[/tex]
The given functions are
[tex]f(x)=3x^2-x+2[/tex]
[tex]g(x)=5x^2-1[/tex]
[tex]f(g(x))=f(5x^2-1)\\\Rightarrow f(5x^2-1)=3(5x^2-1)^2-5x^2+1+2\\\Rightarrow f(g(x))=3(25x^4-10x^2+1)-5x^2+3\\\Rightarrow f(g(x))=75x^4-30x^2+3-5x^2+3\\\Rightarrow f(g(x))=75x^4-35x^2+6[/tex]
So, [tex]f(g(x))=75x^4-35x^2+6[/tex]
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