Question

If `f(n) = 9^-n`, then what is `f(-1/4)`?

Answer 1

`=sqrt3`

Explanation:

put `-1/4` in place of n.

`f(-1/4)`

`=9^(-(-1/4))`

`=9^(1/4)`

`=3^(2*(1/4))`

`=3^(1/2)`

`=sqrt3`

Answer 2

The number in the parentheses to the right replaces `n`. That's to say you must plug the number in the parentheses in place of n in the equation

Explanation:

`f(n) = 9^-n -> n = -1/4`

`f(-1/4) = 9^(-(-1/4)`

`f(-1/4) = 9^(1/4)`

`f(-1/4) = root(4)9`

`f(-1/4) = sqrt(3)`

When they give you the equation and something like `f(x) = 4`, it means they give you the value of y and want you to find the value of x. When they replace x in the parentheses with a number and they give the equation, you're looking for y.

Practice exercises:

1. Evaluate, assuming the equations are of the form `f(x) = y`

a) `f(2) = 2x^2 - 3x + 5`

b) `f(-3) = sqrt(-4x + 4)`

c) `f(x) = 3x - 11, f(x) = 16`

d). `f(x) = 3^x, f(x) = 1/27`

Good luck!