• If f(x) = 4^x then f(x-1)-f(x) equals
  (a) 4
  (b) f(x)
  (c) 2f(x)
  (d) 3f(x)

We are given the function:

f(x) = 4^x

We need to find the value of f(x-1) - f(x).

Step 1: Express f(x-1)
Since f(x) = 4^x, we replace x with (x-1):

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

Step 2: Expand f(x-1) using exponent properties
Using the property a^(m-n) = a^m / a^n, we can rewrite:

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

Step 3: Compute f(x-1) - f(x)
Now, we calculate:

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

Factor out 4^x:

= 4^x (1/4 - 1)

= 4^x (-3/4)

= - (3/4) f(x)

Step 4: Compare with given answer choices
The given options are:
(a) 4
(b) f(x)
(c) 2f(x)
(d) 3f(x)

Since our expression is - (3/4) f(x), none of the options exactly match. There might be an issue with the provided choices, but if we consider the magnitude only, 3f(x) is somewhat close but incorrect due to the coefficient being different.

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

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

=4^x((1/4)-1)

=(-3/4)f(x)