Question # 1 Solution
Answer:
[tex](h-f)(-8)=-229[/tex]
Step-by-step Solution:
Given
[tex]h(r)=-4r^{2}+4[/tex]
[tex]f(r)=2r-7[/tex]
As
[tex](h-f)(r)=h(r)-f(r)[/tex]
[tex](h-f)(r)=-4r^{2}+4-(2r-7)[/tex]
[tex](h-f)(r)=-4r^{2}+4-2r+7)[/tex]
We have to find [tex](h-f)(-8)[/tex]
So,
[tex](h-f)(-8)=-4(-8)^{2}+4-2(-8)+7)[/tex]
[tex](h-f)(-8)=-4(64)+4+16+7[/tex]
[tex](h-f)(-8)=-4(64)+4+16+7[/tex]
[tex](h-f)(-8)=-256+4+16+7[/tex]
[tex](h-f)(-8)=-229[/tex]
∴ [tex](h-f)(-8)=-229[/tex]
Question # 2 Solution
Answer:
∴ [tex](f.p)(9)=38979[/tex]
Step-by-step Solution:
Given
[tex]f(s)=7s-2[/tex]
[tex]p(s)=s^{3}-10s[/tex]
As
[tex](f.p)(s)=f(s).p(s)[/tex]
[tex](f.p)(s)=(7s-2)(s^{3}-10s)[/tex]
[tex](f.p)(s)=7s^4-2s^3-70s^2+20s[/tex]
We have to find [tex](f.p)(9)[/tex]
So,
[tex](f.p)(9)=7\left(9\right)^4-2\left(9\right)^3-70\left(9\right)^2+20\left(9\right)[/tex]
[tex](f.p)(9)=7\cdot \:9^4-2\cdot \:9^3-70\cdot \:9^2+20\cdot \:9[/tex]
[tex](f.p)(9)=9^4\cdot \:7-9^3\cdot \:2-9^2\cdot \:70+180[/tex]
[tex](f.p)(9)=45927-1458-5670+180[/tex]
[tex](f.p)(9)=38979[/tex]
∴ [tex](f.p)(9)=38979[/tex]
Question # 3 Solution
Answer:
[tex](\frac{f}{p})(r)=\frac{11r+8}{r\left(r^2+6\right)}[/tex]
Step-by-step Solution:
Given
[tex]p(r)=r^{3}+6r[/tex]
[tex]f(r)=11r+8[/tex]
We have to find [tex](\frac{f}{p})(r)[/tex]
Using the formula
[tex](\frac{f}{p})(r)=\frac{f(r)}{p(r)}[/tex]
As
[tex]p(r)=r^{3}+6r[/tex]
[tex]f(r)=11r+8[/tex]
So
[tex](\frac{f}{p})(r)=\frac{11r+8}{r^{3}+6r}[/tex]
[tex](\frac{f}{p})(r)=\frac{11r+8}{r\left(r^2+6\right)}[/tex]
∴ [tex](\frac{f}{p})(r)=\frac{11r+8}{r\left(r^2+6\right)}[/tex]
Question # 4 Solution
Answer:
[tex](h-p)(k)=5k^2-3-k^3-8k[/tex]
Step-by-step Solution:
Given
[tex]h(k)=5k^{2}-3[/tex]
[tex]p(k)=k^{3}+8k[/tex]
We have to find [tex](h-p)(k)[/tex]
Using the formula
[tex](h-p)(k)=h(k)-p(k)[/tex]
As
[tex]h(k)=5k^{2}-3[/tex]
[tex]p(k)=k^{3}+8k[/tex]
So
[tex](h-p)(k)=5k^{2}-3-(k^{3}+8k)[/tex]
[tex](h-p)(k)=5k^2-3-k^3-8k[/tex]
∴ [tex](h-p)(k)=5k^2-3-k^3-8k[/tex]
Question # 5 Solution
Answer:
[tex](\frac{p}{g})(11)=\frac{1287}{155}[/tex]
Step-by-step Solution:
Given
[tex]p(b)=b^{3}-4b[/tex]
[tex]g(b)=b^{2}+4b-10[/tex]
We have to find [tex](\frac{p}{g})(11)[/tex]
As
[tex](\frac{p}{g})(b)=\frac{p(b)}{g(b)}[/tex]
[tex](\frac{p}{g})(b)=\frac{b^{3}-4b}{b^{2}+4b-10}[/tex]
So
[tex](\frac{p}{g})(11)=\frac{11^{3}-4(11)}{11^{2}+4(11)-10}[/tex]
[tex](\frac{p}{g})(11)=\frac{1287}{155}[/tex]
∴ [tex](\frac{p}{g})(11)=\frac{1287}{155}[/tex]
Question # 6 Solution
Answer:
[tex](f+g)(x)=x^2+20x-18[/tex]
Step-by-step Solution:
Given
[tex]g(x)=x^{2}+11x-7[/tex]
[tex]f(x)=9x-11[/tex]
We have to find [tex](f+g)(x)[/tex]
As
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex](f+g)(x)=9x-11+(x^{2}+11x-7)[/tex]
[tex](f+g)(x)=9x-11+x^{2}+11x-7[/tex]
[tex](f+g)(x)=x^2+20x-18[/tex]
∴ [tex](f+g)(x)=x^2+20x-18[/tex]
Question # 7 Solution
Answer:
[tex]h(10)+g(10)=-983[/tex]
Step-by-step Solution:
Given
[tex]h(w)=-11w^{2}-7[/tex]
[tex]g(w)=w^{2}+3w-6[/tex]
We have to find [tex]h(10)+g(10)[/tex]
So,
[tex]h(10)=-11(10)^{2}-7[/tex]
[tex]h(10)=-1107[/tex].....[1]
and
[tex]g(10)=10^{2}+3(10)-6[/tex]
[tex]g(10)=124[/tex].....[2]
Adding Equation [1] and Equation [2]
[tex]h(10)+g(10)=-1107+124[/tex]
[tex]h(10)+g(10)=-983[/tex]
∴ [tex]h(10)+g(10)=-983[/tex]
Question # 8 Solution
Answer:
[tex](f+g)(-3)=-6[/tex]
Step-by-step Solution:
Given
[tex]g(b)=b^{2}+9b+10[/tex]
[tex]f(b)=3b+11[/tex]
We have to find [tex](f+g)(-3)[/tex]
As
[tex](f+g)(b)=f(b)+g(b)[/tex]
So
[tex](f+g)(b)=3b+11+b^{2}+9b+10[/tex]
[tex](f+g)(-3)=3(-3)+11+(-3)^{2}+9(-3)+10[/tex]
[tex](f+g)(-3)=-6[/tex]
∴ [tex](f+g)(-3)=-6[/tex]
Question # 9 Solution
Answer:
[tex](f.h)(k)=33k^3+22k-12k^2-8[/tex]
Step-by-step Solution:
Given
[tex]f(k)=-11k+4[/tex]
[tex]h(k)=-3k^{2}-2[/tex]
We have to find [tex](f.h)(k)[/tex]
As
[tex](f.h)(k)=f(k).h(k)[/tex]
So,
[tex](f.h)(k)=(-11k+4).(-3k^{2}-2)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
∵ FOIL means (First, Outer, Inner, Last)
[tex](f.h)(k)=\left(-11k\right)\left(-3k^2\right)+\left(-11k\right)\left(-2\right)+4\left(-3k^2\right)+4\left(-2\right)[/tex]
[tex](f.h)(k)=33k^3+22k-12k^2-8[/tex]
∴ [tex](f.h)(k)=33k^3+22k-12k^2-8[/tex]
Question # 10 Solution
Answer:
[tex]p(-8)-f(-8)=-581[/tex]
Step-by-step Solution:
Given
[tex]p(s)=s^{3}+6s[/tex]
[tex]f(s)=-2s+5[/tex]
We have to find [tex]p(-8)-f(-8)[/tex]
So,
[tex]p(-8)=(-8)^{3}+6(-8)[/tex]
[tex]p(-8)=-560.....[1][/tex]
and
[tex]f(-8)=-2(-8)+5[/tex]
[tex]f(-8)=21.....[2][/tex]
Subtracting Equation [2] from Equation [1]
[tex]p(-8)-f(-8)=-560-21[/tex]
[tex]p(-8)-f(-8)=-581[/tex]
∴ [tex]p(-8)-f(-8)=-581[/tex]
Keywords: function operation
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