$f(x)=4{x}^{2}+5,\text{}g(x)=6x$

Find $(f\circ g)(x)\text{}\text{}\text{},\text{}\text{}\text{}(g\circ f)(x)\text{}\text{}\text{},\text{}\text{}\text{}f(g(-3))\text{}\text{}\text{},\text{}\text{}\text{}g(f(4))$

Ralzereep9h
2022-10-21
Answered

Consider the following functions.

$f(x)=4{x}^{2}+5,\text{}g(x)=6x$

Find $(f\circ g)(x)\text{}\text{}\text{},\text{}\text{}\text{}(g\circ f)(x)\text{}\text{}\text{},\text{}\text{}\text{}f(g(-3))\text{}\text{}\text{},\text{}\text{}\text{}g(f(4))$

$f(x)=4{x}^{2}+5,\text{}g(x)=6x$

Find $(f\circ g)(x)\text{}\text{}\text{},\text{}\text{}\text{}(g\circ f)(x)\text{}\text{}\text{},\text{}\text{}\text{}f(g(-3))\text{}\text{}\text{},\text{}\text{}\text{}g(f(4))$

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Szulikto

Answered 2022-10-22
Author has **22** answers

Step 1

Find $(f\circ g)(x)$

$(f\circ g)(x)=f(g(x))\phantom{\rule{0ex}{0ex}}=f(6x)\phantom{\rule{0ex}{0ex}}=4(6x{)}^{2}+5\phantom{\rule{0ex}{0ex}}=4(36{x}^{2})+5\phantom{\rule{0ex}{0ex}}=144{x}^{2}+5\phantom{\rule{0ex}{0ex}}\text{Find}(g\circ f)(x)\phantom{\rule{0ex}{0ex}}(g\circ f)(x)=g(f(x))\phantom{\rule{0ex}{0ex}}=g(4{x}^{2}+5)\phantom{\rule{0ex}{0ex}}=6(4{x}^{2}+5)\phantom{\rule{0ex}{0ex}}=24{x}^{2}+30\phantom{\rule{0ex}{0ex}}\text{Find}f(g(-3))\phantom{\rule{0ex}{0ex}}f(g(-3))=f(6((-3))\phantom{\rule{0ex}{0ex}}=f(-18)\phantom{\rule{0ex}{0ex}}=4(-18{)}^{2}+5\phantom{\rule{0ex}{0ex}}=4(324)+5\phantom{\rule{0ex}{0ex}}=1296+5\phantom{\rule{0ex}{0ex}}=1301\phantom{\rule{0ex}{0ex}}\text{Find}g(f(4))\phantom{\rule{0ex}{0ex}}g(f(4))=g(4(4{)}^{2}+5)\phantom{\rule{0ex}{0ex}}=g(4(16)+5)\phantom{\rule{0ex}{0ex}}=g(64+5)\phantom{\rule{0ex}{0ex}}=g(69)\phantom{\rule{0ex}{0ex}}=6(69)\phantom{\rule{0ex}{0ex}}=414$

Find $(f\circ g)(x)$

$(f\circ g)(x)=f(g(x))\phantom{\rule{0ex}{0ex}}=f(6x)\phantom{\rule{0ex}{0ex}}=4(6x{)}^{2}+5\phantom{\rule{0ex}{0ex}}=4(36{x}^{2})+5\phantom{\rule{0ex}{0ex}}=144{x}^{2}+5\phantom{\rule{0ex}{0ex}}\text{Find}(g\circ f)(x)\phantom{\rule{0ex}{0ex}}(g\circ f)(x)=g(f(x))\phantom{\rule{0ex}{0ex}}=g(4{x}^{2}+5)\phantom{\rule{0ex}{0ex}}=6(4{x}^{2}+5)\phantom{\rule{0ex}{0ex}}=24{x}^{2}+30\phantom{\rule{0ex}{0ex}}\text{Find}f(g(-3))\phantom{\rule{0ex}{0ex}}f(g(-3))=f(6((-3))\phantom{\rule{0ex}{0ex}}=f(-18)\phantom{\rule{0ex}{0ex}}=4(-18{)}^{2}+5\phantom{\rule{0ex}{0ex}}=4(324)+5\phantom{\rule{0ex}{0ex}}=1296+5\phantom{\rule{0ex}{0ex}}=1301\phantom{\rule{0ex}{0ex}}\text{Find}g(f(4))\phantom{\rule{0ex}{0ex}}g(f(4))=g(4(4{)}^{2}+5)\phantom{\rule{0ex}{0ex}}=g(4(16)+5)\phantom{\rule{0ex}{0ex}}=g(64+5)\phantom{\rule{0ex}{0ex}}=g(69)\phantom{\rule{0ex}{0ex}}=6(69)\phantom{\rule{0ex}{0ex}}=414$

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For the function f whose graph is given, state the following.

(a)$\underset{x\to \mathrm{\infty}}{lim}f(x)$

b)$\underset{x\to -\mathrm{\infty}}{lim}f(x)$

(c)$\underset{x\to 1}{lim}f(x)$

(d)$\underset{x\to 3}{lim}f(x)$

(e) the equations of the asymptotes

Vertical:- ?

Horizontal:-?

(a)

b)

(c)

(d)

(e) the equations of the asymptotes

Vertical:- ?

Horizontal:-?

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Describe the transformations that were applied to

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The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits.

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Answer these question

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Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations.

$y=2\sqrt{x+1}$