Electra Electra
  • 08-11-2024
  • Mathematics
High School

If [tex]f(x) = 3x + 2[/tex], find [tex]f(f^{-1}(14))[/tex].

A. 44
B. 176
C. 4
D. 14

Answer :

gmany gmany
  • 20-12-2023
[tex]f(x)=3x+2\\\\y=3x+2\ \ \ |-2\\\\3x=y-2\ \ \ \ |:3\\\\x=\dfrac{y-2}{3}\to f^{-1}(x)=\dfrac{x-2}{3}[/tex]

[tex]f^{-1}(14)=\dfrac{14-2}{3}=\dfrac{12}{3}=4[/tex]
[tex]f(f^{-1}(14))=3\cdot4+2=12+2=14[/tex]

Answer: d) 14

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