Math  /  Algebra

QuestionSuppose that the functions ss and tt are defined for all real numbers xx as follows. s(x)=4xt(x)=3x1\begin{array}{l} s(x)=4 x \\ t(x)=3 x-1 \end{array}
Write the expressions for (st)(x)(s \cdot t)(x) and (s+t)(x)(s+t)(x) and evaluate (st)(2)(s-t)(-2). (st)(x)=(s+t)(x)=(st)(2)=\begin{array}{r} (s \cdot t)(x)= \\ (s+t)(x)= \\ (s-t)(-2)= \end{array} \square \square \square

Studdy Solution
Substitute x=2 x = -2 into (st)(x) (s - t)(x) :
(st)(2)=(2)+1 (s - t)(-2) = (-2) + 1 (st)(2)=1 (s - t)(-2) = -1
The expressions and evaluation are:
(st)(x)=12x24x(s+t)(x)=7x1(st)(2)=1\begin{array}{r} (s \cdot t)(x) = 12x^2 - 4x \\ (s + t)(x) = 7x - 1 \\ (s - t)(-2) = -1 \end{array}

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