Answer:
[tex]f^{-1}[/tex] (x) = 4x - 40
Step-by-step explanation:
let y = f(x), then rearrange making x the subject
y = [tex]\frac{1}{4}[/tex] x + 10 ( multiply through by 4 to clear the fraction )
4y = x + 40 ( subtract 40 from both sides )
4y - 40 = x
change y back into terms of x, with x being the inverse , that is
[tex]f^{-1}[/tex] (x) = 4x - 40
Answer:
[tex] f^{-1}(x) = 4x - 40 [/tex]
Step-by-step explanation:
To find the inverse of a function, we need to switch the roles of x and y and solve for the new y. Let's find the inverse of the function [tex] f(x) = \dfrac{1}{4}x + 10 [/tex]:
Start with [tex] y = \dfrac{1}{4}x + 10 [/tex].
Switch x and y: [tex] x = \dfrac{1}{4}y + 10 [/tex].
Solve for y:
[tex] x = \dfrac{1}{4}y + 10 [/tex]
Subtract 10 from both sides:
[tex] x - 10 = \dfrac{1}{4}y [/tex]
Multiply both sides by 4 to isolate y:
[tex] 4(x - 10) = y [/tex]
[tex] 4x - 40 = y [/tex]
So, the inverse function is [tex] f^{-1}(x) = 4x - 40 [/tex].
Therefore, the correct answer is [tex] f^{-1}(x) = 4x - 40 [/tex].
