I'm thinking that your typing might be missing some grouping symbols.
You typed:
f(n) = 3-1/2n
This typing means:
\(\displaystyle f(n) = 3 - \frac{1}{2} \cdot n\)
If you mean:
\(\displaystyle f(n) = 3 - \frac{1}{2n}\)
then it must be typed like this:
f(n) = 3 - 1/(2n)
Note the grouping symbols around 2n. They indicate that the denominator is 2n, not 2.
Please clarify your typing.
Likewise, you typed:
(27x^6)^5/3
This typing means:
\(\displaystyle \frac{(27x^6)^5}{3}\)
If the outer exponent is supposed to be 5/3, like this:
\(\displaystyle (27x^6)^{5/3}\)
then you must type it like so:
(27x^6)^(5/3)
Note the grouping symbols around 5/3. They indicate that the outer exponent is 5/3.
Please clarify your typing.
You typed:
240=-3+(n=3)^5/4
No equation has more than one equal sign. Also, is 5/4 an exponent, or is 4 the denominator in a ratio?
Please correct your typing.
Here's how to find the inverse of the linear function f(n), as posted.
f(n) = 3 - 1/2 n
Step 1: Write y instead of f(n)
y = 3 - 1/2 n
Step 2: Switch the n and y variables
n = 3 - 1/2 y
Step 3: Solve for y
n - 3 = 3 - 3 - 1/2 y
n - 3 = -1/2 y
(-2)(n - 3) = (-2)(-1/2 y)
-2n + 6 = y
Step 4: Write y as f-inverse
f[sup:vm9kj1c9]-1[/sup:vm9kj1c9](n) = -2n + 6
Step 5: Check by graphing both f(n) and its inverse, and look for symmetry, OR input the inverse expression -2n + 6 into y = f(n) and verify that it simplifies to y = y.
When you fix your typing, please try to show some work, too. That helps tutors see your mistakes or where you've gone astray.
MY EDIT: Inserted missing negative sign, in my work
