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Use the function f(x)=123x−2f(x)=123x−2 to answer the questions. A: What is f−1(x)f−1(x)? B: What should be done to find the value of xx that makes f(x)=0.75f(x)=0.75? C: For what value of xx does f(x)=0.75f(x)=0.75?

Answer :

Answer:

1) [tex]f^{-1}(x)=\frac{x+2}{123}[/tex]

2) [tex]f(0.02235)=0.75[/tex]

3) [tex]x=0.02235[/tex]

Explanation:

Part 1)

Given that

[tex]f(x)=123x-2[/tex]

To find [tex]f^{-1}(x)[/tex] we put [tex]x=f^{-1}(x)[/tex] in the given function to obtain

[tex]f(f^{-1}(x))=123\times f^{-1}(x)-2\\\\\Rightarrow x=123\times f^{-1}(x)-2(\because f(f^{-1}(x)=x)\\\\\therefore f^{-1}(x)=\frac{x+2}{123}[/tex]

Part 2 and 3)

for [tex]f(x)=0.75[/tex] we put f(x) = 0.75 and then solve for 'x'

[tex]0.75=123\times x -2\\\\\therefore x=\frac{0.75+2}{123}=0.02235[/tex]

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