Question

If f(x) = 3x 1 and f^-1 = x-1/3 , then the ordered pair of f^-1(10) =

Answer 1

f(x)=3x+1
f⁻¹(x)=
`(x-1)/(3)`

f⁻¹(10)=
just subsitute 10 for x in that equaiton
f⁻¹(10)=
`(10-1)/(3)`
f⁻¹(10)=
`(9)/(3)`
f⁻¹(10)=3

orderd pari is (10,3)

Answer 2

The ordered pair of
`\( f^(-1)(10) \)` is
`\((10, 3)\)`.

The notation
`\( f^(-1)(x) \)` represents the inverse function of
`\( f(x) \)`. If
`\( f(x) = 3x + 1 \)`, then to find
`\( f^(-1)(x) \)`, you switch x and y and solve for y :

`\[ x = 3y + 1 \]`

Now, solve for \( y \):

`\[ 3y = x - 1 \]`

`\[ y = (x - 1)/(3) \]`

So,
`\( f^(-1)(x) = (x - 1)/(3) \).`

Now, to find
`\( f^(-1)(10) \)`, substitute
`\( x = 10 \)` into
`\( f^(-1)(x) \)`:

`\[ f^(-1)(10) = (10 - 1)/(3) = (9)/(3) = 3 \]`

Therefore, the ordered pair of
`\( f^(-1)(10) \) is \((10, 3)\)`.