Question

If there is a nonmathematical symbol in the preceding expression, then your browser doesn't have the math symbol font. Please follow the instructions on the WeBWorK front page to install the STIX math fonts. To get around this temporarily, (i) print a hardcopy (the symbols will be there), (ii) in the options box in the right column of this screen, check the formatted option and press the apply options button, or (iii) go to a UITS public cluster (e.g., the Library) and work there.) Find the following:
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

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

c

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

Step-by-step 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

        $g(h(x)) = [x^2 + x + 5 ]^{\frac{1}{4} } + 3$

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

Considering second  question

   Now we are told  h(g(x))

i.e

    $h(g(x)) = [x^{\frac{1}{4} } + 3]^2 + x^{\frac{1}{4} } + 3 + 5$

=> $h(g(x)) = x^{\frac{1}{2} } + 6x^{\frac{1}{4} } + 9+ x^{\frac{1}{4}} + 8$

=>  $h(g(x)) = x^{\frac{1}{2}} + 7x^{\frac{1}{4}} + 17$

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

Considering third question

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

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