Question

if f(x) = 5^x show that f(x+h)=f(x).f(h)

Answer 1

Answer:

The way you read this is 'f of x is equal to 5 to the power of x'. You can substitute any number or variable in for that x as long as you replace x everywhere in the function. For example:

f(y) = 5^y

f(5) = 5^5

f(x+h) = 5^(x+h)

Knowing this, you can now evaluate your longer expression:

f(x+h) - f(x)/h

= 5^(x+h) - 5^x/h

= 5^x * 5^h - 5^x/h

= 5^x * 5^h - 5^x * (1/h)

 

And, by pulling a 5^x out of all terms:

= 5^x (5^h - 1/h)

which is your solution.