Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]g(h(x)) = \sqrt[4]{x^2 + x +5} + 3[/tex]
b
[tex]h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17[/tex]
c
[tex]h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10[/tex]
Step-by-step explanation:
From the question we are told that
[tex]h(x) = x^2 + x + 5[/tex]
and
[tex]g(x) = \sqrt[4]{x} + 3[/tex]
Considering first question
Now we are told g(h(x))
i.e
[tex]g(h(x)) = [x^2 + x + 5 ]^{\frac{1}{4} } + 3[/tex]
=> [tex]g(h(x)) = \sqrt[4]{x^2 + x +5} + 3[/tex]
Considering second question
Now we are told h(g(x))
i.e
[tex]h(g(x)) = [x^{\frac{1}{4} } + 3]^2 + x^{\frac{1}{4} } + 3 + 5[/tex]
=> [tex]h(g(x)) = x^{\frac{1}{2} } + 6x^{\frac{1}{4} } + 9+ x^{\frac{1}{4}} + 8[/tex]
=> [tex]h(g(x)) = x^{\frac{1}{2}} + 7x^{\frac{1}{4}} + 17[/tex]
=> [tex]h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17[/tex]
Considering third question
[tex]h(h(x))= [x^2 + x + 5]^2 + [x^2 + x + 5 ] + 5[/tex]
=> [tex]h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10[/tex]
