Respuesta :
Answer:
f^-1(x) = The quantity of 3x plus 2, divided by 4.
Step-by-step explanation:
Given: f(x) = (4x -2)/3
Which is y = (4x - 2)/3
We have to find the inverse function f^-1 (x)
Replace x by y and y by x, we get
x = (4y - 2)/3
Now find the function y interms of x.
3x = 4y - 2
4y = 3x + 2
y = (3x + 2)/4
f^-1(x) = The quantity of 3x + 2, divided by 4.
Answer is D) f^-1(x) = The quantity of 3x plus 2, divided by 4.
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Answer:
[tex]f^{-1}(x)=\text{The quantity of 3x plus 2, divided by 4}[/tex]
Step-by-step explanation:
Given,
f(x) = The quantity of 4x minus 2, divided by 3,
[tex]\implies f(x) = \frac{4x-2}{3}[/tex] -----(1)
Since, [tex]f^{-1}(x)[/tex] represents the inverse of f(x),
Also, for finding the inverse of a function f(x) we follow the following steps,
Step 1 : Replace f(x) by y,
Step 2 : Interchange x and y,
Step 3 : Isolate y in the left side of the equation,
Step 4 : Replace y by [tex]f^{-1}(x)[/tex]
Now, from equation (1),
[tex]y=\frac{4x-2}{3}[/tex]
By interchanging x and y,
[tex]x=\frac{4y-2}{3}[/tex]
[tex]3x = 4y - 2[/tex]
[tex]-4y = -2 - 3x \implies y = \frac{3x+2}{4}[/tex]
By replacing y by [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)=\frac{3x+2}{4}[/tex]
[tex]\implies f^{-1}(x)=\text{The quantity of 3x plus 2, divided by 4}[/tex]
