Answered

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Find the inverse function

f(x)=3x-1

f^-1 (x)=x+[?]/[ ]

Find The Inverse Function Fx3x1 F1 Xx class=

Sagot :

VirαtKσhli

Answer : [tex]\bf \dfrac{x+1}{3}[/tex]

A function is given to us and we need to find out the inverse of the function . The given function is ,

[tex]\rm \implies f(x) = 3x - 1 [/tex]

Step 1: Substitute y = f(x) :-

[tex]\rm \implies y = 3x -1[/tex]

Step 2: Interchange x and y :-

[tex]\rm \implies x = 3y - 1[/tex]

Step 3: Solve for y :-

[tex]\rm \implies 3y = x + 1 \\[/tex]

[tex]\rm \implies y =\dfrac{x+1}{3} [/tex]

Step 4: Replace y with f-¹(x) :-

[tex]\rm \implies \underline{\boxed{\red{\rm f^{-1}(x) = \dfrac{x+1}{3}}}} [/tex]

Hence the inverse of the function is (x+1)/3.

I hope this helps .

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