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

2 Answers
Feb 20, 2016

#=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#

Feb 20, 2016

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!