If f(x) and f-1(x) are inverse functions of each other and f(x)=2x+5, what is f-1(8)?

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divyamadaan8054 divyamadaan8054 · Answer 1 · 2021-10-25T22:11:46+02:00

The correct option is [tex]B[/tex] and the value of [tex]f^{-1}(8)\;\rm{ is}[/tex] [tex]\frac{3}{2}[/tex].

Given: If [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex] are inverse functions of each other and [tex]f(x)=2x+5[/tex].

According to question:

[tex]f(x)=2x+5\\[/tex]

[tex]y=2x+5\\x=\frac{y-5}{2}\\[/tex]

[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Now,

[tex]f^{-1}(8)=\frac{8-5}{2}\\f^{-1}(8)=\frac{3}{2}[/tex]

Hence, the value of [tex]f^{-1}(8)\;\rm{is}\;\frac{3}{2}[/tex].

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abidemiokin abidemiokin · Answer 2 · 2021-11-08T13:50:28+01:00

The required inverse of the function at when x = 8 is 3/2: Option B is correct

Given the function g(x)=2x+5, first we need to find the inverse of the function:

Let y = g(x)

y= 2x + 5

Replace y with x

x = 2y + 5

Make y the subject of the formula

2y = x - 5

y = (x - 5)/2

Hence the inverse of the expression is f^{-1}x = (x - 5)/2

Substitute x = 8 into the result

f^{-1}(8) = (8 - 5)/2

f^{-1}(8) = 3/2

Hence the required inverse of the function at when x = 8 is 3/2

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