Question 965270

{{{f(x)=4x}}} and {{{g(x)=x^4-8}}}

a. {{{(g*f)(-2)}}}

since {{{(f*g)(x)=f(x)*g(x)}}}, you are multiplying the functions: 

{{{(f*g)(-2)=4x*(x^4-8)}}}

{{{(f*g)(-2)=4x^5-32x)}}}

{{{(f*g)(-2)=4(-2)^5-32(-2))}}}

{{{(f*g)(-2)=4(-32)+64}}}

{{{(f*g)(-2)=-128+64}}}



b. {{{(f*g)(2)}}}

{{{(f*g)(2)=4x*(x^4-8)}}}

{{{(f*g)(2)=4x^5-32x)}}}

{{{(f*g)(2)=4(2)^5-32(-2))}}}

{{{(f*g)(2)=4(32)+64}}}

{{{(f*g)(2)=128+64}}}

{{{(f*g)(2)=192}}}



c. {{{(g*f)(x)}}} simplify

{{{(f*g)(x)=4x*(x^4-8)}}}

{{{(f*g)(x)=4x^5-32x)}}}


d. {{{(f*g)(x)}}}=> will be same as c. by commutative property of multiplication