Answer:
The values are
a) [tex]h(3)=91[/tex]
b) [tex]h(-1)=3[/tex]
c) [tex]h(-x)=x^4+x^2+1=h(x)[/tex]
d) [tex]h(3a)=9a^2(9a^2+1)+1[/tex]
Step-by-step explanation:
Given that the function h is defined by
[tex]h(x)=x^4+x^2+1[/tex]
To find
a) h(3)
Put x=3 in the given function [tex]h(x)=x^4+x^2+1[/tex] we get
[tex]h(3)=3^4+3^2+1[/tex]
[tex]=81+9+1[/tex]
[tex]=91[/tex]
Therefore [tex]h(3)=91[/tex]
b) h(-1)
Put x=-1 in the given function [tex]h(x)=x^4+x^2+1[/tex] we get
[tex]h(-1)=(-1)^4+(-1)^2+1[/tex]
[tex]=1+1+1[/tex]
[tex]=3[/tex]
Therefore [tex]h(-1)=3[/tex]
c) h(-x)
Put x=-x in the given function [tex]h(x)=x^4+x^2+1[/tex] we get
[tex]h(-x)=(-x)^4+(-x)^2+1[/tex]
[tex]=x^4+x^2+1[/tex]
[tex]=h(x)[/tex]
Therefore [tex]h(-x)=x^4+x^2+1=h(x)[/tex]
d) h(3a)
Put x=3a in the given function [tex]h(x)=x^4+x^2+1[/tex] we get
[tex]h(3a)=(3a)^4+(3a)^2+1[/tex]
[tex]=3^4.a^4+3^2.a^2+1[/tex]
[tex]=81a^4+9a^2+1[/tex]
[tex]=9a^2(9a^2+1)+1[/tex]
Therefore [tex]h(3a)=9a^2(9a^2+1)+1[/tex]
