Problem: If f(x)=4xf(x)=4^{x}f(x)=4x then f(x+1)−f(x)f(x+1)-f(x)f(x+1)−f(x) equals:
Answer Choices:
A. 444
B. f(x)f(x)f(x)
C. 2f(x)2 f(x)2f(x)
D. 3f(x)3 \mathrm{f}(\mathrm{x})3f(x)
E. 4f(x)4 \mathrm{f}(\mathrm{x})4f(x) Solution:
f(x+1)−f(x)=4x+1−4x=4x(4−1)=3⋅4x=3f(x)f(x+1)-f(x)=4^{x+1}-4^{x}=4^{x}(4-1)=3 \cdot 4^{x}=3 f(x)f(x+1)−f(x)=4x+1−4x=4x(4−1)=3⋅4x=3f(x).