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Need explanation 20 points
The function f is such that f(x) = 2x - 6
Find f^-1(x)

Sagot :

TheAnimeGirlidn

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Explanation :

GIVEN :

  • f(x) = 2x - 6

TO FIND :

  • Inverse of f(x) i.e [tex]f ^{ - 1} (x)[/tex]

SOLUTION :

FOLLOW THESE THREE STEPS :

  • LET Y = f(x)

[tex] \longrightarrow \tt{y = 2x - 6}[/tex]

[tex] \longrightarrow{ \tt{ \: 2x - 6 = y}}[/tex]

  • MAKE X A SINGLE TERM IN LHS SIDE

[tex] \longrightarrow{ \tt{2x = y + 6}}[/tex]

[tex] \longrightarrow{ \tt{x = \frac{y + 6}{2} }}[/tex]

  • INTERCHANGE THE VALUE OF X AND Y

[tex] \longrightarrow{ \tt{y = \frac{x + 6}{2} }}[/tex]

Hence ,

[tex] \boxed{ \boxed{ {f}^{ - 1} (x) = \sf{ \bold{ \frac{x + 6}{2} }}}}[/tex]

Hope I helped!

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