Suppose that f(x)=8x^2?4x and g(x)=7x+1. For each function h given below, find a

Question

Suppose that f(x)=8x^2?4x and g(x)=7x+1. For each function h given below, find a formula for h(x) and the domain of h. Note: When entering interval notation in WeBWorK, use I for ?, -I for ??, and U for the union symbol. If the set is empty, enter "{}" without the quotation marks. (I just need help with the last two H(x))

(1 point) Suppose that For each function h given below, find a formula for h(x and the domain of h Note: When entering interval notation in WeBWork, use i for oo -l for -oOL and U for the union symbol. If the set is empty, enter "th without the quotation marks. h(x) 392x 2+84x+4 Domain (-1, l) 56x A 2-28x+1 Domain (-1, l) Domain I, Domain (-1, l)

Explanation / Answer

we have given f(x)=8x^24x and g(x)=7x+1

A) h(x)=(fog)(x)= f(g(x))=f(7x+1)=8(7x+1)^24(7x+1)=8*(49x^2+1+14x)-28x-4=392x^2+8+112x-28x-4=392x^2+84x+4

h(x)=392x^2+84x+4

the domain of h(x) is (-I,I),it takes all real values and defines the function

B) we have given h(x)=(gof)(x)

h(x)=(gof)(x)=g(f(x))=g(8x^24x)=7(8x^24x)+1=56x^2-28x+1

h(x)=56x^2-28x+1

the domain of h(x) is (-I,I),it takes all real values and defines the function

C) we have given h(x)=(fof)(x)

h(x)=(fof)(x)=f(f(x))=f(8x^24x)=8(8x^24x)^24(8x^24x)=8(64x^4+16x^2-64x^3)-32x^2+16x

=512x^4+128x^2-512x^3-32x^2+16x=512x^4-512x^3+96x^2+16x

h(x)=512x^4-512x^3+96x^2+16x

the domain of h(x) is (-I,I),it takes all real values and defines the function

D) we have given h(x)=(gog)(x)

h(x)=(gog)(x)=g(g(x))=g(7x+1)=7(7x+1)+1=49x+7+1=49x+8

h(x)=49x+8

the domain of h(x) is (-I,I),it takes all real values and defines the function

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