Question

Re-write the equation without the h component.

a. f(x)=2(3)^(x-2)+2


b. f(x)=1/2(4)^(x+1)

Answer 1

`f(x) = 2[(3^x)/(9)] + 2`

`f(x) = 8(4)^x`

Explanation:

Given

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

`f(x) = (1)/(2)(4)^(x+2)`

Required

Remove the h component

In a function, the h component is highlighted as:

`f(x) = a^(x+h)`

So, we have:

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

Split the exponents using the following law of indices:

`a^m/a^n = a^(m-n)`

`f(x) = 2*(3^x)/(3^2) + 2`

`f(x) = 2*(3^x)/(9) + 2`

`f(x) = 2[(3^x)/(9)] + 2`

The h component has been removed

`f(x) = (1)/(2)(4)^(x+2)`

Split the exponent using the following law of indices

`a^(m+n) =a^m * a^n`

So, we have:

`f(x) = (1)/(2)(4)^x * 4^2`

Express 4^2 as 16

`f(x) = (1)/(2)(4)^x * 16`

Divide 16 by 2

`f(x) = 8(4)^x`