To find the inverse of this function, we need to perform some steps.
f(x) = 2x + 9
Replace f(x) with y.
y = 2x + 9
Swap x and y.
x = 2y + 9
Solve for y.
Subtract both sides by 9.
x - 9 = 2y
Divide both sides by 2.
(x - 9)/2 = y
Replace y with f^-1(x)
The inverse of the function f(x)=2x+9 is [tex]f^{-1}(x) = \frac{x-9}{2}[/tex]
To determine the inverse of the given function f(x) = 2x + 9
First,
Let y = f(x)
That is,
y = 2x + 9
Now, make x the subject of the equation
To make x the subject of the equation
[tex]y = 2x + 9[/tex]
First, subtract 9 from both sides
That is
[tex]y -9= 2x + 9-9[/tex]
Then,
[tex]y - 9 =2x[/tex]
∴ [tex]2x = y -9[/tex]
Now, divide both sides by 2
We get
[tex]\frac{2x}{2} =\frac{y-9}{2}[/tex]
[tex]x=\frac{y-9}{2}[/tex]
Now, rewrite as f⁻¹(x) by replacing y by x
That is,
[tex]f^{-1}(x) = \frac{x-9}{2}[/tex]
Hence, the inverse of the function f(x)=2x+9 is [tex]f^{-1}(x) = \frac{x-9}{2}[/tex]
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