Question

Describe and correct the error, given the functions f(x)=3x-5 and g(x)=1/3-4/3x1. g(-3)=1/3-4/3(3)=1/3-4=-3 2/32. f(1)=1/3-4/3(1)=1/3-4/3=-3/3= -1Show as much work possible please

Answer 1

we have the following:

$\begin{gathered} f\mleft(x\mright)=3x-5 \\ g\left(x\right)=\frac{1}{3}-\frac{4}{3}x \\ \end{gathered}$

therefore,

1.

$\begin{gathered} g\left(-3\right)=\frac{1}{3}-\frac{4}{3}\cdot(3) \\ g\left(-3\right)=\frac{1}{3}-4 \\ g\left(-3\right)=-3\frac{2}{3} \end{gathered}$

correct form: the value of x is -3 and not 3

$\begin{gathered} g\left(-3\right)=\frac{1}{3}-\frac{4}{3}\cdot(-3) \\ g\left(-3\right)=\frac{1}{3}-(-4) \\ g\left(-3\right)=\frac{1}{3}+4 \\ g\left(-3\right)=\frac{1+12}{3}=\frac{13}{3} \end{gathered}$

2.

$\begin{gathered} f\mleft(1\mright)=\frac{1}{3}-\frac{4}{3}\cdot(1) \\ f(1)=\frac{1}{3}-\frac{4}{3} \\ f(1)=-1 \end{gathered}$

correct form: It must be evaluated in the function f(x) = 3x -5, and not in the function g(x)

$\begin{gathered} f(1)=3\cdot(1)-5 \\ f(1)=3-5 \\ f(1)=-2 \end{gathered}$