If f(x)=6x^3+5x,g(x)=3x^2+5,and h(x)=9x^2-8 what is the degree of f(g(h(x))) awer choices are a.2 b.3 3.7 4.12
Accepted Solution
A:
To find f(g(h(x))), we need to find g(h(x)) first. To do that we are going to evaluate the function g(x) at h(x): We know that [tex]h(x)=9x^2-8[/tex] and [tex]g(x)=3x^2+5[/tex] [tex]g(h(x))=g(9x^2-8)=3(9x^2-8)^2+5[/tex] [tex]=3(81x^4-144x^2+64)+5[/tex] [tex]=243x^4-432x^2+192+5[/tex] [tex]=243x^4-432x^2+197[/tex]
Now that we know that [tex]g(h(x))=243x^4-432x^2+197[/tex], to find [tex]f(g(h(x)))[/tex] we are going to evaluate [tex]f[/tex] at [tex]243x^4-432x^2+197[/tex] [tex]f(g(h(x)))=f(243x^4-432x^2+197)[/tex] [tex]f(243x^4-432x^2+197)=6(243x^4-432x^2+197)^3[/tex][tex]+5(243x^4-432x^2+197)[/tex]