Can you please help me find the functions?

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Answer 1 · 2018-05-14T18:33:43

$(g+k)(x)=g(x)+k(x) = x-3 + 2x = 3x-3$

$(hk)(x) = h(x)k(x) = (x^2-9)(2x) = 2x^3 - 18x$

$h(g(x)) = h( x-3) = (x-3)^2 -9 = x^2 - 6x$

$h(g(k(x))) = h(g(2x)) = (2x)^2 - 6(2x) = 4x^2 - 12 x$

Answer 2 · 2018-05-14T18:37:31

$f(x)=x$
$g(x)=x-3$
$h(x)=x^2-9$
$k(x)=2*x$

1.
$(g+k)(x)=g(x)+k(x)=$

$=x-3+2*x=3*(x-1)$

2.
$(h*k)(x)=h(x)*k(x)$

$=(x^2-9)*(2*x)=2*x^3-18x$

3.
$h(g(x))=(g(x))^2-9=(x-3)^2-9=$

$=x^2-2*3*x+9-9=x^2-6*x$

4.
We can use the) result of 3. replacing $x$ with $k(x)$

$h(g(k(x)))=(k(x))^2-6*k(x)=(2*x)^2-6*2*x=$

$=4*x^2-12x$