Question

Seriously confused! Will medal!

Answer 1

Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f−1(3).

2
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8

Answer 2

I know that something to the ^-1 power is basically the recipricol.. like 5^-1 would be 1/5 but how would I do the fraction in this problem?

Answer 3

f^-1(x) is not the same as 1/f(x)
The easiest method to solve this is to write y instead of f(x).
Then you solve the equation for x in terms of y.

f(x) = (4x+1)/3
y=(4x+1)/3
3y=4x+1
.
.
.
x=(3y-1)/4

f^-1(x)=(3x-1)/4
f^-1(3)=2

Answer 4

Equivalently, you can plug in y = 3 and solve for x to get the same answer

y=(4x+1)/3
3=(4x+1)/3
...
...
...
x = 2

Answer 5

The notation \(\Large f^{-1}(x)\) means "f inverse" or "the inverse of f(x)"

like jualbafer wrote, it is NOT the same as \(\LARGE \frac{1}{f(x)}\)

yes it's confusing because the negative one exponent has 2 different meanings