Question

Write the exponential function f(x)=-3*4^(1-x) in the form f(x)=ab^x

Answer 1

f(x)=-3*4^(1-x)

= -3 * 4^1 * 4^(-x)

= -12 4^(-x)

= -12 (1/4)^x

Answer 2

`f(x) = -12((1)/(4))^x`

Explanation:

Given function,

`f(x)=-3* 4^(1-x)`

Using the product rule of exponent i.e.
`a^m.a^n=a^(m+n)`

`f(x) = -3 * 4 * 4^(-x)`

`f(x) = -12* 4^(-x)`

Using power of power rule of exponent i.e.
`(a^b)^c = a^(bc)`

`f(x) = -12(4^(-1))^x`

Since,
`a^m =(1)/(a^(-m))`

`\implies f(x) = -12((1)/(4))^x`

Which is the required form of
`f(x) = ab^x`

Where,

a = -12, b = 1/4