if (s(x)=x - 7) and (t(x)=4x^{2}-x + 3), which expression is equivalent to ((tcirc s)(x))?\n(4(x - 7)^{2}-x…

if (s(x)=x - 7) and (t(x)=4x^{2}-x + 3), which expression is equivalent to ((tcirc s)(x))?\n(4(x - 7)^{2}-x - 7+3)\n(4(x - 7)^{2}-(x - 7)+3)\n((4x^{2}-x + 3)-7)\n((4x^{2}-x + 3)(x - 7))

if (s(x)=x - 7) and (t(x)=4x^{2}-x + 3), which expression is equivalent to ((tcirc s)(x))?\n(4(x - 7)^{2}-x - 7+3)\n(4(x - 7)^{2}-(x - 7)+3)\n((4x^{2}-x + 3)-7)\n((4x^{2}-x + 3)(x - 7))

Answer

Explanation:

Step1: Recall function - composition definition

The composition ((t\circ s)(x)=t(s(x))).

Step2: Substitute (s(x)) into (t(x))

Given (s(x)=x - 7) and (t(x)=4x^{2}-x + 3), we substitute (x) in (t(x)) with (s(x)). So (t(s(x))=4(s(x))^{2}-s(x)+3).

Step3: Replace (s(x)) with its expression

Since (s(x)=x - 7), then (t(s(x))=4(x - 7)^{2}-(x - 7)+3).

Answer:

(4(x - 7)^{2}-(x - 7)+3) (the second option)