f(x)=x−3 and \(\displaystyle{g{{\left({x}\right)}}}={4}{x}^{2}−{3}{x}−{9}{g{{\left({x}\right)}}}={4}{x}^{{2}}−{3}{x}−{9}\). Find composite function \(\displaystyle{f}∘{g}\) and \(\displaystyle{g}∘{f}\)

Your answer

asked 2021-01-15

asked 2021-12-17

Assume f and g are differentiable on their domains with \(\displaystyle{h}{\left({x}\right)}={\left({f}{o}{g}\right)}{\left({r}\right)}\). Suppose the equation of the line tangent to the graph of g at the point \(\displaystyle{\left({4},{7}\right)}\) is\(\displaystyle{y}={3}{x}–{5}\) and the equation of the line tangent to the graph of f at \(\displaystyle{\left({7},{9}\right)}\) is \(\displaystyle{y}=-{2}{x}+{23}\).

(a) Calculate \(\displaystyle{h}{\left({4}\right)}\) and \(\displaystyle{h}'{\left({4}\right)}\).

(b) Determine an equation of the line tangent to the graph of h at the point on the graph where \(\displaystyle{x}={4}\).

(a) Calculate \(\displaystyle{h}{\left({4}\right)}\) and \(\displaystyle{h}'{\left({4}\right)}\).

(b) Determine an equation of the line tangent to the graph of h at the point on the graph where \(\displaystyle{x}={4}\).

asked 2021-06-13

1. Who seems to have more variability in their shoe sizes, men or women?

a) Men

b) Women

c) Neither group show variability

d) Flag this Question

2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?

a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation

b) The estimate n-1 is never used to calculate the sample variance and standard deviation

c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population

d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)

a) Men

b) Women

c) Neither group show variability

d) Flag this Question

2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?

a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation

b) The estimate n-1 is never used to calculate the sample variance and standard deviation

c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population

d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)

asked 2021-05-11

Determine the domains of the given rational functions.

\(\displaystyle\frac{{4}}{{{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}}}\)

\(\displaystyle\frac{{4}}{{{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}}}\)

asked 2021-06-30

\(\displaystyle\frac{{4}}{{{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}}}\)

asked 2021-06-20

Determine the domains of the given rational functions.

\(\displaystyle\frac{{{x}^{{2}}-{9}}}{{{x}^{{3}}-{x}}}\)

\(\displaystyle\frac{{{x}^{{2}}-{9}}}{{{x}^{{3}}-{x}}}\)

asked 2021-05-13

Find derivatives for the functions. Assume a, b, c, and k are constants.

\(\displaystyle{D}{\left({p}\right)}={e}^{{{p}^{{{2}}}}}+{5}{p}^{{{2}}}\)

\(\displaystyle{D}{\left({p}\right)}={e}^{{{p}^{{{2}}}}}+{5}{p}^{{{2}}}\)