# Given f(x) = 3x + 4 and g(x) = sqrt x, calculate g(f)

Question
Rational functions
Given $$\displaystyle{f{{\left({x}\right)}}}={3}{x}+{4}{\quad\text{and}\quad}{g{{\left({x}\right)}}}=\sqrt{{x}}$$, calculate g(f)

2021-02-13
f(x)=3x+4
$$\displaystyle{g{{\left({x}\right)}}}=\sqrt{}$$
$$\displaystyle{g{{\left({f{{\left({x}\right)}}}\right)}}}=\sqrt{{{3}{x}+{4}}}$$

### Relevant Questions

The function $$\displaystyle{f{{\left({x}\right)}}}={x}\frac{{\left({64}-{x}^{{2}}\right)}^{{1}}}{{2}}$$ satisfies the hypotheses of Rolle's Theorem on the interval [-8,8]. Find all values of that satisfy the conclusion of the theorem.
a.) + 1, AND -1
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My answer. The intervals do match and equal zero so Rolles theorem can work.
Second I found the derivative maybe thats where I can't solve this problem.
The derivative that I got was $$\displaystyle{64}-{x}^{{2}}+\frac{{x}}{\sqrt{{{64}-{x}^{{2}}}}}$$ maybe i did wrong on the simplifying. I at least tried hopefully some one can explain as much as possible with every single step because I can figure out the algebra part.
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