Question

If s(x)=x-7 and t(x)=4x^2-x+3 which expression is equivalent to (txs)(x)?

Answer 1

For this case we have by definition that:

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

In this case we must find$(t * s) (x),$ so:

($(t * s) (x) = t (x) * s (x) = (4x ^ 2-x + 3) * (x-7) =$

We must apply distributive property that states that:

$(a + b) (c + d) = ac + ad + bc + bd$

So:

$(4x ^ 2-x + 3) * (x-7) = 4x ^ 3-28x ^ 2-x ^ 2 + 7x + 3x-21 = 4x ^ 3-29x ^ 2 + 10x-21$

Answer:

$4x^3-29x^2+10x-21$