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Find the value of b in the function f(x) ax + b if f^-1(3)=2 and f^-1(-3) = 6, where f^-1(x) is the inverse of the function f(x).
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Find The Value Of B In The Function Fx Ax B If F132 And F13 6 Where F1x Is The Inverse Of The Function Fx B class=

Sagot :

Using inverse functions, it is found that b = 6.

Inverse function:

  • To find the inverse function, we exchange x and y in the original function, then isolate f.

In this problem, the function is:

[tex]y = f(x) = ax + b[/tex]

To find the inverse:

[tex]x = ay + b[/tex]

[tex]ay = x - b[/tex]

[tex]y = \frac{x - b}{a}[/tex]

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

At x = 3, the inverse is 2, hence:

[tex]2 = \frac{3 - b}{a}[/tex]

[tex]2a = 3 - b[/tex]

[tex]a = \frac{3 - b}{2}[/tex]

At x = -3, the inverse is 6, hence:

[tex]6 = \frac{-3 - b}{a}[/tex]

[tex]6a = -3 - b[/tex]

[tex]a = \frac{-3 - b}{6}[/tex]

Equaling:

[tex]\frac{3 - b}{2} = \frac{-3 - b}{6}[/tex]

[tex]6(3 - b) = 2(-3 - b)[/tex]

[tex]18 - 6b = -6 - 2b[/tex]

[tex]4b = 24[/tex]

[tex]b = \frac{24}{4}[/tex]

[tex]b = 6[/tex]

To learn more about inverse functions, you can take a look at https://brainly.com/question/8824268

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