Exponential Function Prove

[greatwhiteshark]

Exponential Function Prove

1) If f(x) = a^x, show that f(x+h) - f(x)/h = a^x [(a^h - 1/h)]

2) If f(x) = a^x, show that f(-x) = 1/f(x)

What are the steps necessary to solve questions 1 and 2?

 

[tkhunny]

Exponential Function Prove

1) If f(x) = a^x, show that f(x+h) - f(x)/h = a^x [(a^h - 1/h)]

2) If f(x) = a^x, show that f(-x) = 1/f(x)

What are the steps necessary to solve questions 1 and 2?

Looks like plug-and-chug to me.

2) f(x) = a^x

f(-x) = a^(-x) = (a^x)^(-1) = [f(x)]^(-1) = 1/f(x)

Do the substitutions suggested on the first one and see if you can simplify or manipulate into the suggested shape.

 

[greatwhiteshark]

okay

I will try to do the same to question 1.