Question

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a. g(h(x))=_______
b. h(g(x))=_______
c. h(h(x))=_______

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

`g(h(x)) = \sqrt[4]{x^2 + x +5} + 3`

b

`h(g(x))  = √(x)  + 7\sqrt[4]{x} + 17`

c

`h(h(x)) =  [x^2 + x + 5 ]^2 + x^2 + x + 10`

Explanation:

From the question we are told that

`h(x) =  x^2  + x  + 5`

and

`g(x) = \sqrt[4]{x} + 3`

Considering first question

Now we are told g(h(x))

i.e

`g(h(x)) =  [x^2 + x + 5 ]^{(1)/(4) } + 3`

=>
`g(h(x)) = \sqrt[4]{x^2 + x +5} + 3`

Considering second question

Now we are told h(g(x))

i.e

`h(g(x)) =  [x^{(1)/(4) } + 3]^2 +  x^{(1)/(4) } + 3 + 5`

=>
`h(g(x)) =  x^{(1)/(2) } + 6x^{(1)/(4) } + 9+ x^{(1)/(4)}  + 8`

=>
`h(g(x))  = x^{(1)/(2)} + 7x^{(1)/(4)} + 17`

=>
`h(g(x))  = √(x)  + 7\sqrt[4]{x} + 17`

Considering third question

`h(h(x))= [x^2 + x + 5]^2 + [x^2 + x + 5 ] +  5`

=>
`h(h(x)) =  [x^2 + x + 5 ]^2 + x^2 + x + 10`