defazajx

2021-09-09

Given $f\left(x\right)=4{x}^{2}-3\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}g\left(x\right)=6-\frac{1}{2}{x}^{2}$
b.

Velsenw

Obtain the composite function .
The given two functions are $f\left(x\right)=4{x}^{2}-3\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}g\left(x\right)=6-\frac{1}{2}{x}^{2}$.
To obtain the composite function , substitute $f\left(x\right)$ for x in the function $g\left(x\right)$.
The composite function is obtained as $\frac{192{x}^{4}-288{x}^{2}+107}{32{x}^{4}-48{x}^{2}+18}$ from the calculation given below:
$\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)$
$=g\left(4{x}^{2}-3\right)$
$=6-\frac{1}{2{\left(4{x}^{2}-3\right)}^{2}}$
$=6-\frac{1}{2\left(16{x}^{4}+9-24{x}^{2}\right)}$
$=\frac{6×\left(32{x}^{4}+18-48{x}^{2}\right)-1}{32{x}^{4}+18-48{x}^{2}}$
$\frac{192{x}^{4}-288{x}^{2}+107}{32{x}^{4}-48{x}^{2}+18}$
Obtain the value of .
The composite function is obtained as $\frac{192{x}^{4}-288{x}^{2}+107}{32{x}^{4}-48{x}^{2}+18}$.
To obtain the value of , substitute 2 in place of x in the composite function $=\frac{192{x}^{4}-288{x}^{2}+107}{32{x}^{4}-48{x}^{2}+18}$.
The value of is obtained as 5.997 from the calculation given below:
$\left(g\circ f\right)\left(x\right)=\frac{192{x}^{4}-288{x}^{2}+107}{32{x}^{4}-48{x}^{2}+18}$
$\left(g\circ f\right)\left(2\right)=\frac{192{\left(2\right)}^{4}-}{}$

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