Mathematics: Suppose that the functions f and g are defined for all real numbers x as follows. f(x) = x - 5, g(x) = 2(x) + 6 write the expressions for (f*g)(x) and (f-g)(

The first question is correct, yes 50%The second question is also correct, 1/4Hope this helps....

Suppose that the functions f and g are defined for

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15.01.2022

$(f*g)(x)=2x^{2}-4x-30\\$

$(f-g)(x)=-(x+11)\\$

Step-by-step explanation:

the expression (f*g)(x) can be expanded as follows

$(f*g)(x)=f(x)*g(x)\\$

since f(x)=x-5,g(x)=2x+6

Hence

$(f*g)(x)=f(x)*g(x)\\(f*g)(x)=(x-5)*(2x+6)\\(f*g)(x)=2x^{2}+6x-10x-30\\(f*g)(x)=2x^{2}-4x-30\\$

also the expansion for (f-g)(x) is express as

$(f-g)(x)=f(x)-g(x)\\$

also since

f(x)=x-5,g(x)=2x+6 then when we substitute values, we have

$(f-g)(x)=(x-5)-(2x+6)\\(f-g)(x)=x-5-2x-6\\(f-g)(x)=-x-11\\(f-g)(x)=-(x+11)\\$

For this type of operation kindly note the below expansions

$(f*g)(x)=f(x)*g(x)\\$

$(f-g)(x)=f(x)-g(x)\\$

$(f+g)(x)=f(x)+g(x)\\$

$(f/g)(x)=f(x)/g(x)\\$

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