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)(x)..

Question

asked Mar 16, 2021 67.9k views

1 Answer

Bewildered · Answer 1 · 2021-03-22T06:40:39+0000

Answer:

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

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

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

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

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

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

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