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If f(x) = 7x + 9x + 2, then f-1(x) = __________.f -1(x) = 16(x - 2)f -1(x) = (x - 2)/16f -1(x) = (1/16)(x + 2)f -1(x) = (1/8)(x - 2)

If fx 7x 9x 2 then f1x f 1x 16x 2f 1x x 216f 1x 116x 2f 1x 18x 2 class=

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Solution

Given the function as shown below

[tex]f(x)=7x+9x+2[/tex]

To find the inverse of f(x), we will set it to y first

[tex]\begin{gathered} y=7x+9x+2 \\ y=16x+2 \end{gathered}[/tex]

Swap the position of y and x, then solve for y

[tex]x=16y+2[/tex][tex]\begin{gathered} x-2=16y \\ \frac{x-2}{16}=y \\ f^{-1}(x)=y \\ f^{-1}(x)=\frac{x-2}{16} \end{gathered}[/tex]

Hence, the inverse of the function f(x) is:

[tex]f^{-1}(x)=\frac{x-2}{16}[/tex]

Option B is the right choice