To find (fg)(x0)\left(\frac{f}{g}\right)(x_0)(gf)(x0), substitute x0=−6x_0 = -6x0=−6 into both f(x)f(x)f(x) and g(x)g(x)g(x) and compute the quotient. Given f(x)=x−1f(x) = x - 1f(x)=x−1 and g(x)=(x+1)∗(x+3)g(x) = (x + 1)*(x + 3)g(x)=(x+1)∗(x+3), f(−6)=−7f(-6) = -7f(−6)=−7 and g(−6)=15g(-6) = 15g(−6)=15. Thus, (fg)(−6)=−0.467\left(\frac{f}{g}\right)(-6) = -0.467(gf)(−6)=−0.467.
rac{f}{g}\) To find all values not in the domain of racfg rac{f}{g}racfg, solve the equation g(x)=0g(x) = 0g(x)=0. The values of xxx for which g(x)=0g(x) = 0g(x)=0 are [-3, -1], which are excluded from the domain of rac<functiongat0xffff7821fa30><functionfat0xffff7821f010> rac<function g at 0xffff7821fa30><function f at 0xffff7821f010>rac<functiongat0xffff7821fa30><functionfat0xffff7821f010>.
The quotient (fg)(−6)\left(\frac{f}{g}\right)(-6)(gf)(−6) is -0.467, and the values excluded from the domain of rac<functiongat0xffff7821fa30><functionfat0xffff7821f010> rac<function g at 0xffff7821fa30><function f at 0xffff7821f010>rac<functiongat0xffff7821fa30><functionfat0xffff7821f010> are [-3, -1].
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