What is the inverse of the function $f(x) = -3x + 3$ ?

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Answer 1 · 2016-01-11T12:30:41

$f^-1(x) = (3-x)/3 quad$ Step by step working is shown below.

To find inverse function follow the following steps

Step 1: Swap $x$ and $y$
Step 2: Solve for $y$
Step 3: The result you got is the inverse function. Write in proper notation.

Let us see this with the given problem.

Let $y=f(x) = -3x+3$

$y=-3x+3$

Step 1: Swap $x$ and $y$
$x=-3y+3$

Step 2: Solve for $y$

$x-3 = -3y quad$ On subtracting 3 from both sides.
$(x-3)/-3= y quad$ Dividing by -3 on both sides isolates $y$

$(3-x)/3 = y$

Step 3: Writing it in proper notation

$f^-1(x) = (3-x)/3$

Answer 2 · 2016-01-11T12:32:10

$bar(f(x)) = 1-x/3$
$color(white)("XXXXXXXXX")$ where $bar(f(x))$ denotes the inverse of $f(x)=-3x+3$

Let $bar(f(x))$ be the inverse of $f(x)=-3x+3$

By definition of inverse
$color(white)("XXX")f(bar(f(x)))=color(blue)(x)$

But if $f(color(red)(x)) = -3color(red)(x)+3$
then
$color(white)("XXX")f(color(red)(bar(f(x))))=-3color(red)(bar(f(x)))+3$

Therefore
$color(white)("XXX")-3bar(f(x))+3=color(blue)(x)$

$color(white)("XXX")-3bar(f(x)) = x-3$

$color(white)("XXX")bar(f(x)) = (x-3)/(-3)$

$color(white)("XXX")bar(f(x))=1-x/3$

What is the inverse of the function f(x) = -3x + 3f(x) = -3x + 3?