find the sum, difference, product and quotient of these functions: f(x)=2^x, g(x)= 2^(x-1)

Question

find the sum, difference, product and quotient of these functions: f(x)=2^x, g(x)= 2^(x-1)

Answer 1

f(x) + g(x) = 2^x + 2^(x-1) = 2*2^(x-1)+ 2^(x-1) = 2^(x-1) (2+1)= 

3 * 2^(x-1) 

 

f(x) - g(x) = 2^x - 2^(x-1) = 2*2^(x-1)- 2^(x-1) = 2^(x-1) (2-1)=
   2^(x-1)

 

f(x) * g(x) = 2^x * 2^(x-1) = 2^[x + (x-1) ]= 2^(2x-1)

 

f(x) / g(x) = 2^x / 2^(x-1) = [2*2^(x-1)]/[2^(x-1) ]= 2

 

 

Answer 2

Monira,

 

Can you think of a way to rewrite g(x) so the exponent is simplified? Hint: It's a property of exponents that, e.g., 5^x * 5² = 5^x+2.

 

Once you've rewritten g(x), it will probably be easier to find the sum, difference, product, and quotient of the two functions.

 

I'll give you some hints for finding each.

 

Sum

 

Note that 5^-1 is equal to 1/5.

 

Knowing that, what do you think 2^x - 2^x-1 is?

 

Difference

 

Try doing something similar to the sum.

 

Product

 

Try following the logic in my first hint (5^x * 5² = 5^x+2).

 

Quotient

 

It's also a property of exponents that you can write 5^x/5² as 5^x * 5^-2. Rewriting that way may make it easier to solve.

 

Good luck!