QuestionIf $s(x)=x-7$ and $t(x)=4 x^{2}-x+3$ , which expression is equivalent to $(t \circ s)(x) ?$ $4(x-7)^{2}-x-7+3$ $4(x-7)^{2}-(x-7)+3$ $\left(4 x^{2}-x+3\right)-7$ $\left(4 x^{2}-x+3\right)(x-7)$

Studdy Solution

STEP 1

1. We are given two functions, $s(x) = x - 7$ and $t(x) = 4x^2 - x + 3$ .
2. We need to find the expression for the composition of functions $(t \circ s)(x)$ , which means $t(s(x))$ .

STEP 2

1. Substitute $s(x)$ into $t(x)$ .
2. Simplify the resulting expression.

STEP 3

Substitute $s(x) = x - 7$ into $t(x) = 4x^2 - x + 3$ .
$t(s(x)) = t(x - 7) = 4(x - 7)^2 - (x - 7) + 3$

STEP 4

Simplify the expression $4(x - 7)^2 - (x - 7) + 3$ .
Notice that the expression is already in a simplified form that matches one of the given options.
The equivalent expression for $(t \circ s)(x)$ is:
$\boxed{4(x-7)^{2}-(x-7)+3}$

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