Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9

Question

asked Nov 18, 2022 80.0k views

2 Answers

Joseph Holsten · Answer 1 · 2022-11-21T23:22:32+0000

Given:

The function is

$f(x)=\left((1)/(3)\right)^x$

To find:

The missing values for a, b, and c in the given table.

Solution:

We have,

$f(x)=\left((1)/(3)\right)^x$

At x=-2,

$f(-2)=\left((1)/(3)\right)^(-2)$

$a=\left(3\right)^(2)$
$\left[\because \left((a)/(b)\right)^(-n)=\left((b)/(a)\right)^(n)\right]$

a=9

At x=-1,

$f(-1)=\left((1)/(3)\right)^(-1)$

$b=\left(3\right)^(1)$
$\left[\because \left((a)/(b)\right)^(-n)=\left((b)/(a)\right)^(n)\right]$

b=3

At x=0,

$f(0)=\left((1)/(3)\right)^(0)$

c=1
$\left[\because a^0=1, a\\eq 0\right]$

Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.