Question

1. the machines are in order so one machines output is the next machines input. what is the third machines output if the first machines input is ( x = - 5 ) first machine ( f(x)=2x ) second machine ( g(x)=\frac{7x + 5}{x} ) third machine ( h(x)=x^{2}-4x + 10 ) 11. for which of the functions below, does ( f(-3)=20 ) ? show work under each choice. circle all that apply. a. ( f(x)=x+(-17) ) b. ( f(x)=x^{2}+11 ) c. ( f(x)=5x + 5 )

Explanation:

Step1: Find the output of the first machine

Substitute \(x = - 5\) into \(f(x)=2x\).
\(f(-5)=2\times(-5)=-10\)

Step2: Use the output of the first machine as the input of the second machine

Substitute \(x=-10\) into \(g(x)=\frac{7x + 5}{x}\).
\(g(-10)=\frac{7\times(-10)+5}{-10}=\frac{-70 + 5}{-10}=\frac{-65}{-10}=\frac{13}{2}\)

Step3: Use the output of the second machine as the input of the third machine

Substitute \(x = \frac{13}{2}\) into \(h(x)=x^{2}-4x + 10\).

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Answer:

\(26.25\)